نشریه جبرهای اندازه و کاربردها
پیاپی 1 (پاییز 1402)

Assume that G is a compact Hausdorff topological group and H is a closed subgroup of G. In this paper, we will define the notion of relative commutativity degree for the subgroup H, which will be a generalization of the concept of relative commutativity degree in the case of finite groups. Then we will prove some properties of relative commutativity degree, that hold for finite groups, for these groups. In particular, we will derive an upper bound for the relative commutativity degree and state and prove a structural theorem for groups that have this upper bound. Additionally, we will provide some examples of compact infinite groups for which the mentioned bounds hold.

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.

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.

In this paper, the stability of duals and approximate duals of discrete frames, continuous frames and generalized frames in Hilbert spaces and Hilbert C*-modules under the action of bounded operators is considered. It is shown that under some conditions, duals and approximate duals are stable under the action of bounded operators. Especially, the stability of duals and approximate duals under the morphisms of Hilbert C*-modules is studied.

In this paper, we first define the concept of diagonal measure corresponding to an invariant measure of a compact dynamical system and will investigate some of its properties. Finally, we show that, integrating a suitable function with respect to the diagonal measure results in the metric entropy of a compact dynamical system.

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.

Orlicz spaces, as a very important generalization of Lebesgue spaces, were proposed more than 100 years ago and were first introduced by Z. W. Birnbaum and W. Orlicz. After that, another generalization of Lebesgue spaces with symbols X^p instead of L^p was introduced in which X is a Banach function space. In this article, another generalization of Lebesgue spaces is investigated, which includes both previous generalizations. Although this generalization and preliminary studies of it were published in a scientific report in 1988, effective research on this generalization was done 15 years ago. Due to the fact that in this generalization a convex and Young function Φ is placed instead of function |.|^p and a Banach function space X is placed instead of space L^1, in this article, taking into account the conditions of the function Φ we will check properties of generalized Orlicz space X^Φ.

In this paper, we state Rado's theorem, Ramsey families, and their connections with ergodic theory and combinatorial problems. We discuss the historical development of these concepts since their inception to how some problems in the fields of combinatorics and number theory were formulated and solved, particularly through the lens of dynamical systems. We also address some open questions in this field.

In this paper, we first introduce a two-level hierarchical model with a linear structure.  We use the moment, maximum likelihood, and SURE estimators to obtain the regression coefficients shrinkage estimators. Since, regression models have vast applications in high-dimensional datasets, using sparsity assumption, we discuss the asymptotic properties of the regression estimators under L_2 error norm and L_1 penalty norm.

We show that there is a one-to-one correspondence (up to isomorphism) between maximal subgroups of a Clifford semigroup and isotropy subgroups of its universal groupoid. We prove that a Clifford semigroup is a union of amenable subgroups if and only if its universal groupoid is amenable. We give an example of an amenable Clifford semigroup that its universal groupoid is not amenable.

In this paper, some new results on resolutions of the identity, atomic systems and frame-like systems for subspaces of a Hilbert space are obtained. In particular, their sums and their stability under the action of invertible operators are considered

In this paper, we introduce a new homological notion related to biprojective Banach algebras, namely A^{**}-biprojective Banach algebras. We study the relation between this new notion and the other homological notions, such as amenability, pseudo-amenability and inner amenability. Also, we investigate this new notion on certain Banach algebras such as group algebras, Lipschitz algebras and triangular Banach algebras.