مجله موجکها و جبر خطی
سال هشتم شماره 3 (Autumn and Winter 2021)

In this paper, numerical solution of linear Fuzzy Fredholm integral equations of the second kind is investigated, using CAS wavelets by applying Galerkin method. In order to illustrate the accuracy of the method, some numerical examples are presented. In comparison to the results obtained by applying the Legendre and Chebyshev wavelet method, our results, specifically in the case of integral equations with periodic functions, exhibit higher accuracy. Thus, applying CAS wavelets to these integral equations are recommended.

In this paper, using the notion of Hermite-Hadamard type of isosceles orthogonality (HH-I-orthogonality) and its unitary version, we provide a new characterization of inner product spaces. In fact, we give a necessary and sufficient condition weaker than the homogeneity of HH-I-orthogonality in real normed linear space X, whose dimension is at least three, under which the norm of X comes from an inner product.

A nonnegative real matrix is called ‎row‎ stochastic if sum of all entries in each row is one. For vectors ‎$‎x, y \in R_n‎$‎, it is said that ‎$‎x‎$‎ is left-right matrix majorized by ‎$‎y‎$ ‎and ‎write ‎‎$‎x\prec_{rl} y‎$‎ if for some row stochastic matrices ‎$‎A,B‎$‎; ‎$‎x=yA‎$ ‎and ‎‎$‎x‎^‎t=By^t‎$‎. A linear operator ‎$‎T : ‎\mathbb{R}_n‎\longrightarrow ‎‎\mathbb{R}_n‎$‎‎‎ is said to be a linear preserver of a given relation ‎$‎‎\mathcal{R}‎‎$‎ if ‎$‎x‎\mathcal{R}‎y‎$‎‎‎ implies that ‎$‎T(x)‎\mathcal{R}T(y)‎$‎‎‎.‎ In this parer we characterize the linear preservers of ‎$‎\prec_{rl}‎$‎ from ‎$‎\mathbb{R}_n‎$‎ to $‎\mathbb{R}_n‎$‎. ‎In fact, w‎e show that the linear preservers of ‎$‎\prec_{rl}‎$‎ from ‎$‎ mathbb{R}_n‎$‎ to $‎\mathbb{R}_n‎$ are the same as the linear preservers of ‎$‎\prec_{m}‎$‎ from ‎$‎\mathbb{R}_n‎$‎ to $‎\mathbb{R}_n‎$ for ‎$‎n\leq 3‎$‎; but for ‎$‎n\geq 4‎$‎; they are not the same.

In this paper, we obtain a norm model for the unitary orbit of an irreducible matrix x in terms of the linear and matrix valued polynomials. Consequently, we prove that the unitary orbit of an irreducible matrix x is the set of all matrices z such that the norm of matrix valued polynomials of order one in terms of the matrix x is equal to the norm of matrix valued polynomials of order one in terms of the matrix z.

The aim of this paper is to investigate the closed-ness of the range of the modular operators in Hilbert C*-modules. We present the conditions that, the reverse order law for the closed range modular operators and modular projections be holds. Also, we prove that, for modular operators A and B with closed ranges, if BA=0 then A†B† =0. Moreover, we give a novel characterization of the normal modular operators in Hilbert C*-modules.

The algebra A is generated by idempotents if the generated algebra by its idempotents equal to A. In this paper we show that if N is a finite nest on a complex Hilbert space H, then the nest algebra A 1g N is generated by its idempotents. Then we obtain some results by applying our main result. Especially, we give a simple proof for that is any finite nest algebra A 1g N, is a zero product determined algebra.

In this paper, while reviewing the concept of quantum operator systems and their representation theorems, we study the quantum C*- envelope of a quantum operator system.

In this paper, we will introduce and study “Continuous weaving K-frames in Hilbert spaces”.We first introduce a useful result for the production of these frames and then examine them under the influence of a boundary operator.Due to the basic and useful use of different types of frames in restoring some deleted information in data transfer issues, we have dedicated the end of the paper to the conditions of setting the frame under the removal of some members of the measure space and we will see that, this is related to the discrete K-frames.

In this paper, we study the theory of dilation in operator algebras by introducing theorems that have the same theme. We propose some important theorems and point out the existence of the same proof idea for such theorems.

In this note, a counterpart of the well-known Block Triangularization Theorem for Real Algebras of Numerical Matrices, i.e., matrices with real, complex, or quaternion entries, is presented. Thereby, some consequences of the Block Triangularization Theorem for Real Algebras of Numerical Matrices are presented.

Let B_s (H) be the Jordan algebra of all bounded selfadjont operators on a separable Hilbert space H. In this paper we investigate and characterize all additive, one to one and onto maps \phi:B_s(H)\longrightarrow B_s(H) that preserve Drazin inverse of operators. We conclude that if for every projection operator P, we have the set \phi(\mathbb{R}P) be a subset of \mathbb{R}\phi(P) and also the relation \phi(PB_s(H)P)= \phi(P)B_s(H)\phi(P) is satisfied, then there is a unitary or anti-unitary operator U:H\rightarrow H, such that \phi(T)=UTU^*, for all T\in B_s(H).

Wavelet-Galerkin method is a powerful tool for the numerical solution of partial differential equations. The main aim of this paper is, by combining the finite difference method with the wavelet-Galerkin method, to solve some first order partial differential equation and we also show that this method can be useful for analytical solution of such equations.