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جستجوی مقالات مرتبط با کلیدواژه

c$k$-frame

در نشریات گروه ریاضی
تکرار جستجوی کلیدواژه c$k$-frame در نشریات گروه علوم پایه
  • Elnaz Osgooei *, Asghar Rahimi
    In this study, motivating the explanation of Esmeral, Ferrer, and Wagner, similar findings regarding frames in Hilbert spaces were attempted to be extended to Krein spaces. The objective of the paper appears to be to explore the properties and characteristics of frames, particularly in the context of Krein spaces and various categories of operators. The paper discusses the implications of removing elements from a frame and the conditions under which a sequence remains a frame or becomes incomplete. In particular, it is shown that the value of $\left[f_{j}, S^{-1}f_{j}\right]$ is important in recognizing which sequences $\{f_{k}\}_{k=1}^{\infty}$ qualify as frames or incomplete sets. Subsequently,  the importance of the synthesis operator in characterizing frames and establishing the connection between frame bounds and the properties of the synthesis operator was investigated. Additionally, for certain operators U, conditions have been established under which the sequence $\{Uf_{k}\}_{k=1}^{\infty}$ will be a frame sequence, provided that $\{f_{k}\}_{k=1}^{\infty}$ is already a frame. The concept of a Riesz basis in Krein spaces was introduced, followed by determining the conditions equivalent for a frame to qualify as minimal, a Riesz basis, or an exact frame. Lastly, a clear structure for the duals of frames in Krein spaces has been established. It was discovered that the dual frames of the sequence $\{f_{k}\}_{k=1}^{\infty}$ correspond to the families $\{JV\delta_{k}\}_{k=1}^{\infty}$ where $V:(L^{2}(\mathbb{N}, [.,.]_{\tilde{J}})\rightarrow (K, [.,.]_{J})$ serves as a bounded left inverse of $T_{0}^{*}$ and $J$ is a fundamental symmetry in $K$.
    Keywords: Krein Space, Frame, Dual, Indefinite Inner Product, Riesz Basis, *-Inverse
  • Narjes Banitaba, S. Mohammad Moshtaghioun*

    In this article, we obtain some stability property of continuous K-g-frames, along with some characterization of them, with respect to synthesis and frame operators. Also, we obtain a continuous K-g-dual of Parseval continuous K-g-frames in Hilbert spaces, with some dual properties.


    Keywords: K-G-Dual, Continuous K-G-Frame, C-K-G-Operator
  • E. Rajput, N. Kumar Sahu*

    In 2016, Bemrose et al. introduced the weaving frames in a Hilbert space which is influenced by a problem in distributed signal processing. Ghobadzadeh et al. proposed the idea of woven frames in Hilbert $C^*$-modules in 2018. The authors studied and investigated numerous elementary properties of weaving frames in Hilbert $C^*$-modules. As K-frames and standard frames deviate in several perspectives, we acquaint the notion of weaving K-frames and an atomic system for weaving K-frames in Hilbert $C^*$-modules. Inside this script, we explore weaving K-frames from an operator theoretic point of view. We provide an identical interpretation for weaving K-frames and characterize weaving K-frames in terms of bounded linear operators. We also inspect the invariance of woven Bessel sequences under an adjointable operator.

    Keywords: Hilbert C*-Module, Frame, K-Frame, Woven Frame, K-Woven Frame, Adjoint Operator
  • Purbita Jana *

    This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with the L-topological system and L-topological space are established.

    Keywords: Geometric Logic, Frame, Topological System, $L$-Topology
  • Mohammad Ali Hasankhani Fard *
    A g-phase retrievable frame is a $\lambda$-phase retrievable frame in finite dimensional Hilbert space $\mathcal{H}_n$, where $\lambda$ is an special function, which is called phase coefficient function. In this paper we study the Lipschitz analysis of the nonlinear map $\alpha_{\lambda,{\mathcal{F}}}:\widehat{\mathcal{H}_n}\longrightarrow\mathbb{F}^m, \ \ \ \alpha_{\lambda,{\mathcal{F}}}(\hat{x}):=\begin{bmatrix}\lambda\left( \left\langle {x,f_k}\right\rangle\right)\end{bmatrix}_{1\leq k\leq m}$, where $\widehat{\mathcal{H}_n}$ is the quotient space corresponding to a special equivalence relation on $\mathcal{H}_n$ with respect to phase coefficient function $\lambda$,  $\mathcal{F}=\{f_k\}_{k=1}^m$ is a $\lambda$-phase retrievable frame for $\mathcal{H}_n$, $\mathbb{F}=\mathbb{R}$ for real Hilbert space $\mathcal{H}_n$ and $\mathbb{F}=\mathbb{C}$ for complex Hilbert space $\mathcal{H}_n$.
    Keywords: Frame, Phase Coefficient Function, Phase Retrievable Frame, $, Lambda$-Phase Retrievable Frame, G-Phase Retrievable Frame, Lipschitz Continuous Function
  • Mojgan Mahmoudi *, Amir H. Nejah

    In this paper we study topological spaces, frames, and their confrontation in the presheaf topos of $M$-sets for a monoid $M$. We introduce the internalization, of the frame of open subsets for topologies, and of topologies of points for frames, in our universe. Then we find functors between the categories of topological spaces and of frames in our universe.We show that, in contrast to the classical case, the obtained functors do not have an adjoint relation for a general monoid, but in some cases such as when $M$ is a group, they form an adjunction. Furthermore, we define and study soberity and spatialness for our topological spaces and frames, respectively. It is shown that if $M$ is a group then the restriction of the adjunction to sober spaces and spatial frames becomes into an isomorphism.

    Keywords: Topological Space, Frame, $M$-Set, Topos, Sober Space, Spatial Frame
  • Inderasan Naidoo *

    This is the first in a series of survey papers featuring the mathematical contributions of Themba Dube to pointfree topology and ordered algebraic structures. We cover Dube’s distinguished career and benefactions to the discipline with the early beginnings in nearness frames. We envelope the essential aspects of Dube’s work in structured frames. The paper radars across the initial themes of nearness, metrization, and uniform structures that Dube conceives and presents in his independent and joint published papers. Pertinent subcategories of these structured frames are discussed. We also feature Dube’s imprints on certain categorical aspects of his work on βL, λL, υL and ßL.

    Keywords: Nearness, Uniform Frame, Locally Fine, Paracompact, Booleanization, Completion, Cauchy Completion
  • Mohammadali Hasankhani Fard *

    In this paper a class of Gabor frames with time shift parameter $a>0$, frequency shift parameter $b>0$ and bounded compactly supported generator function $g$ such that $supp\ g\subseteq\left[\left(k+2\right)a-\frac{2}{b},ka+\frac{1}{b}\right]$ or $supp\ g\subseteq\left[\left(k+1\right)a-\frac{1}{b},ka+\frac{1}{b}\right]$, where $k$ is an integer number is introduced. In particular, a sufficient condition on a function $g\in C_c^+\left( \mathbb{R}\right) $ with $supp\ g\subseteq\left[\left(k+2\right)a-\frac{2}{b},ka+\frac{1}{b}\right]$ and positive decreasing derivative $g^\prime$ on $\left(ka-\frac{1}{b},\left( k+2\right)a \right)$, that make $\left\{E_{mb}T_{na}g\right\}_{m,n\in\mathbb{Z}}$ into a Gabor frame, is given.

    Keywords: Frame, Dual Frame, Gabor System, Gabor Frame
  • فرخنده تخته*
    در این مقاله، R-دوگان ها نسبت به پایه های ریس را در فضاهای هیلبرت مورد مطالعه قرار می دهیم. به ویژه، برای دنباله های بسل با استفاده از یک عملگر مزدوج خطی مفهوم R-دوگان ها را مورد بررسی قرار می دهیم و نتایج  و ساختارسازی هایی را برای قاب ها، پایه های ریس و دنباله های ریس برحسب R-دوگان ها به دست می آوریم.
    کلید واژگان: فضای هیلبرت، قاب، R-دوگان، پایه ریس
    Farkhondeh Takhteh *
    In this paper, we consider the concept of R-duality with respect to Riesz bases. In particular, we study the concept of R-duality with respect to Riesz bases, constructed by anti-linear operators, for Bessel sequences. Using these anti-linear operators, we give some characterizations for frames and Riesz bases.
    Keywords: Hilbert Space, Frame, R-Dual, Riesz Basis
  • Hassan Jamali *, Reza Pourkani
    ‎In this paper, we delve into frame theory to create an innovative iterative method for resolving the operator equation $ Lu=f $. In this case, $ L:H\rightarrow H $, a bounded, invertible, and self-adjoint linear operator, operates within a separable Hilbert space denoted by $H$. Our methodology, which is based on the GMRES projective method, introduces an alternate search space, which brings another dimension to the problem-solving process. Our investigation continues with the assessment of convergence, where we look at the corresponding convergence rate. This rate is intricately influenced by the frame bounds, shedding light on the effectiveness of our approach. Furthermore, we investigate the ideal scenario in which the equation finds an exact solution, providing useful insights into the practical implications of our work.
    Keywords: Operator Equation, Frame, Preconditioning, GMRES Iteration, Convergence Rate
  • Reza Ahmadi, Gholamreza Rahimlou

    In this article, first we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gcframes. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa

    Keywords: Hilbert space, Lebesgue integral, trace classoperator, frame, measure space
  • فرخنده تخته*
    در این مقاله، مفهوم R-دوگان های قاب ها در فضاهای هیلبرت را مورد مطالعه قرار می دهیم. به ویژه، R-دوگان های تعریف شده نسبت به پایه های ریس مورد توجه قرار می گیرند و ساختارسازی هایی از قاب ها و پایه های ریس برحسب R-دوگان های آن ها نسبت به پایه های ریس ارایه می شوند.
    کلید واژگان: فضای هیلبرت، دنباله بسل، قاب، R-دوگان، پایه ریس
    Farkhondeh Takhteh *
    In this paper, the concept of R-duality with respect to Riesz bases is focused. In particular, some characterizations for frames and Riesz bases in terms of their R-dual sequences with respect to Riesz bases are given.
    Keywords: Hilbert space, Bessel sequence, frame, R- dual, Riesz basis
  • محمدرضا فرمانی*، امیر خسروی

    در این مقاله،  قاب ها، پایه ریس و پایه ریس مدولار در *C-مدول های هیلبرت را  مورد مطالعه قرار می دهیم. نشان خواهیم داد که برخی از خواص پایه های ریس از  یک فضای هیلبرت به  پایه های ریس  مدولار قابل انتقال هستند. سپس قاب های درهم تنیده،  قاب های P-درهم تنیده  و  قاب های CP- درهم تنیده در *C-مدول های هیلبرت مورد مطالعه و بحث قرار خواهند گرفت. علاوه بر این، برخی از نتایج به دست آمده در فضاهای هیلبرت را به *C-مدول های هیلبرت،  تعمیم خواهیم داد و  نتایجی دررابطه با آشفتگی و افزونگی قاب های  درهم تنیده ارایه خواهیم کرد.

    کلید واژگان: قاب، قاب درهم تنیده، P-قاب درهم تنیده، *C-مدول هیلبرت
    Mohammad Reza Farmani *, Amir Khosravi

    In this paper, we investigate woven frames, P-woven  and CP-woven frames in Hilbert C*-modules. We also study frames, Riesz bases, and modular Riesz bases in Hilbert C*-modules. We show that modular Riesz bases share some properties with Riesz bases in Hilbert spaces. We generalize some main results in Hilbert spaces to Hilbert C*-modules and we get some results about perturbation and redundancy of woven frames.

    Keywords: frame, woven frame, P-woven frame, Hilbert C*-module
  • زینب جوادی*
    در این مقاله، نتایجی در مورد شبه دوگان ها، دوگان های تقریبی و دوگان های قاب های پیوسته و قاب های گسسته در فضاهای هیلبرت به دست می آ یند. به ویژه، شبه دوگان ها، دوگان های تقریبی و دوگان هایی که با قرار گرفتن یک عملگر کران دار بین عملگر ترکیب و تحلیل قاب ساخته می شوند، مورد توجه قرار می گیرند. نشان داده می شود که درصورت برقراری برخی از شرایط، آنها تحت عملگرهای کران دار و اختلال های کوچک پایا هستند.
    کلید واژگان: فضای هیلبرت، قاب، دوگان، شبه دوگان، دوگان تقریبی
    Zeinab Javadi *
    In this paper, we obtain some results for pseudo-duals, approximate duals, and duals of continuous and discrete frames in Hilbert spaces. In particular, the ones constructed by bounded operators inserted between the synthesis and analysis operators of a frame are considered. We show that under some conditions, they are stable under the action of bounded operators and small perturbations.
    Keywords: Hilbert space, frame, dual, pseudo-dual, approximate dual
  • M. Abedi *
    ‎The set $\mathcal{C}_{c}(L)=\Big\{\alpha\in\mathcal{R}L‎ : ‎\big\vert\{ r\in\mathbb{R}‎ : ‎\coz(\alpha-{\bf r})\ne 1\big\}\big\vert\leq\aleph_0 \Big\}$ is a sub-$f$-ring of $\mathcal{R}L$‎, ‎that is‎, ‎the ring of all continuous real-valued functions on a completely regular frame $L$.‎ ‎The main purpose of this paper is to continue our investigation begun in \cite{a} of extending ring-theoretic properties in $\mathcal{R}L$ to‎ ‎the context of completely regular frames by replacing the ring $\mathcal{R}L$ with the ring $\mathcal{C}_{c}(L)$ to the context of zero-dimensional frames.‎ ‎We show that a frame $L$ is a $CP$-frame if and only if $\mathcal{C}_{c}(L)$ is a regular ring if and only if every ideal of $\mathcal{C}_{c}(L)$ is pure if and only if $\mathcal{C}_c(L)$ is an Artin-Rees ring if and only if every ideal of $\mathcal{C}_c(L)$ with the Artin-Rees property is an Artin-Rees ideal if and only if the factor ring $\mathcal{C}_{c}(L)/\langle\alpha\rangle$ is an Artin-Rees ring for any $\alpha\in\mathcal{C}_{c}(L)$ if and only if every minimal prime ideal of $\mathcal{C}_c(L)$ is an Artin-Rees ideal.‎
    Keywords: frame, CP-frame, P-frame, Artin-Rees property, regular ring
  • PRASENJIT GHOSH*, Tapas Samanta

    The notion of a K-frame in n-Hilbert space is presented and some of their characterizations are given. We establish stability condition of K-frame in n-Hilbert space under some perturbations. We verify that sum of two K-frames is also a K-frame in n-Hilbert space. Also, the concept of tight K-frame in n-Hilbert space is described and some properties of its are going to be established.

    Keywords: Frame, K-Frame, N-Normed Space, N-Inner Product Space
  • اعظم شکاری، محمدرضا عبدالله پور*

    در این مقاله، نتایج جدیدی را درباره - قاب های پیوسته ثابت می کنیم. همچنین مفهوم  -پایه های ریس پیوسته را معرفی کرده و شرطی لازم و کافی را ارایه خواهیم داد که تحت این شرط،   به یک   -پایه ریس پیوسته تبدیل شود. در نهایت برای عملگر برد بسته ی   ، ثابت می کنیم که تحت شرایطی خاص، F  یک - پایه ریس است اگر و تنها اگر فقط یک دوگان داشته باشد که در آن، ، تصویر متعامد از H به توی R (K) ، یعنی برد عملگر K می باشد.

    کلید واژگان: K-قاب پیوسته، K-پایه ریس پیوسته، K-دوگان پیوسته، K-قاب پیوسته ریس گونه
    Azam Shekari, MohammadReza Abdollahpour *

    In this paper, we prove some new results about cK-frames. Also, we introduce the concept of cK-Riesz basis and we provide a necessary and sufficient condition under which $F$ is a cK-Riesz basis. Finally, for the closed range operator $K \in B(\mathcal{H})$, we prove that under some conditions, $\pi_{R(K)}F$ is a cK-Riesz basis if and only if it has only one dual, where $\pi_{R(K)}$ is the orthogonal projection from $\mathcal{H}$ onto $R(K)$, i.e., the range of $K$.

    Keywords: ck-frame, cK-Riesz bases, ck-dual, Riesz-type cK-frame
  • فرانسیس ومفو، اتین روموالد تیمگوا آلومو، سلستین لیلی
    Francis Woumfo *, Etienne Romuald Temgoua, Celestin Lele

    The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of a state residuated lattice $(L, \varphi)$ and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice $\mathcal{SI}(L)$ is a Boolean algebra.

    Keywords: State ideal, frame, Residuated lattice
  • Habib Shakoory, Reza Ahmadi*, Gholamreza Rahimlou, Vahid Sadri

    Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we can define analysis, synthesis and frame operators with representation space compatible for (C,C')-Controlled g-fusion frames, which even yield a reconstruction formula. Also, some useful concepts such as Q-dual and perturbation are introduced and investigated.

    Keywords: G-fusion frame, Controlled fusion frame, Controlled g-fusion frame, Q-dual
  • Mostafa Abedi *, AliAkbar Estaji

    Motivated by definitions of countable completely regular spaces and completely below relations of frames, we define what we call a $c$-completely below relation, denoted by $\prec\!\!\prec_c$, in between two elements of a frame. We show that $a\prec\!\!\prec_c b$ for two elements $a, b$ of a frame $L$ if and only if there is $\alpha\in\mathcal{R}L$ such that $\coz\alpha\wedge a=0$ and $\coz(\alpha-{\bf1})\leq b$ where the set $\{r\in\mathbb{R} : \coz(\alpha-{\bf r})\ne 1\}$ is countable. We say a frame $L$ is a $c$-completely regular frame if $a=\bigvee \limits_{x\prec\!\!\prec_ca}x$ for any $a\in L$. It is shown that a frame $L$ is a $c$-completely regular frame if and only if it is a zero-dimensional frame. An ideal $I$ of a frame $L$ is said to be $c$-completely regular if $a\in I$ implies $a\prec\!\!\prec_c b$ for some $b\in I$. The set of all $c$-completely regular ideals of a frame $L$, denoted by ${\mathrm{c-CRegId}}(L)$, is a compact regular frame and it is a compactification for $L$ whenever $it$ is a $c$-completely regular frame. We denote this compactification by $\beta_cL$ and it is isomorphic to the frame $\beta_0L$, that is, Stone-Banaschewski compactification of $L$. Finally, we show that open and closed quotients of a $c$-completely regular frame are $c$-completely regular.

    Keywords: frame, c-completely regular frame, space, c-completely below relation, c-completely regular ideals, zero-dimensional frame, compactification of frame
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