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Linear and Topological Algebra - Volume:10 Issue: 2, Spring 2021

Journal of Linear and Topological Algebra
Volume:10 Issue: 2, Spring 2021

  • تاریخ انتشار: 1400/05/06
  • تعداد عناوین: 7
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  • M. Sohrabi * Pages 79-91

    ‎In this paper‎, ‎we give an explicit formula for the Moore-Penrose inverse of $W$‎, ‎denoted by $W^{dag}$‎, ‎on $L^2(Sigma)$‎. ‎As an application‎, ‎we give a characterization for some operator classes that are weaker than $p$-hyponormal with $W^{dag}$‎. ‎Moreover‎, ‎we give specific examples illustrating these classes‎.

    Keywords: Moore-Penrose inverse, weighted composition operator, polar decomposition, partial isometry, hyponormal operator
  • H. Alimorad *, Sh. Abdolmohammadi Pages 93-99
    In this paper, a new method for solving coupled complex matrix equations is applied. In this method, we change the problem into a real equation system by using the multiplication properties of complex numbers. This new problem can be solved easily. Numerical examples are given to show the efficiency of the new method.
    Keywords: Complex matrix, Coupled system, Imaginary part, Kronecker product, permutation matrix, real part
  • M. Gulistan, I. Beg *, A. Malik Pages 101-116

    In this paper, based on embedding approach three numerical methods namely Richardson, Gauss-Seidel, and successive over relaxation (SOR) have been developed to solve bipolar neutrosophic system of linear equations. To check the accuracy of these newly developed schemes an example with exact and iterative solution is given.

    Keywords: Richardson iterative method, Gauss Seidel method, Successive Over Relaxation (SOR) method, Bipolar neutrosophic system of linear equations
  • P. Ghosh *, T. K. Samanta Pages 117-130
    In this paper, our aim is to introduce the concept of a frame in $n$-Hilbert space and describe some of its properties. We further discuss tight frame relative to $n$-Hilbert space. At the end, we study the relationship between frame and bounded linear operator in $n$-Hilbert space.
    Keywords: $n$-inner product space, $n$-normed space, pseudo-inverse, Frame, tight frame
  • A. Nikseresht * Pages 131-143

    The phenomenon of defectless extensions is a classical notion in the framework of valued fields and valued vector spaces in valuation theory. The aim of this paper is to study various results regarding this concept and its applications.

    Keywords: Valued fields, defectless extensions, algebraic field extensions
  • M. Hashemi *, M. Polkouei Pages 145-152
    In this paper, by using the relations and properties of some classes of two generator 2-groups of nilpotency class two, we find the order of automorphism group of these groups.
    Keywords: Automorphism groups, 2-groups, nilpotency class
  • M. H. Harbau *, B. Ali Pages 153-177
    In this paper, we introduce a linesearch algorithm for solving fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings and pseudomonotone equilibrium problem in reflexive Banach space. Using the linesearch method, we prove a strong convergence of the iterative scheme to a common point in the set of solutions of some equilibrium problem and common fixed point of the finite family of Bregman quasi asymptotically nonexpansive multivalued mappings with out imposing Bregman Lipschitz condition on the bifunction $g$ as used by many authors in the extragradient method. Our results improve and generalize many recent results in the literature.
    Keywords: Bregman-quasi-asymptotically multivalued nonexpansive mappings, strong convergence, pseudomonotone equilibrium problem, Legendre function