فهرست مطالب
Journal of Linear and Topological Algebra
Volume:8 Issue: 2, Spring 2019
- تاریخ انتشار: 1398/03/11
- تعداد عناوین: 7
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Pages 85-95Frames generalize orthonormal bases and allow representation of all the elements of the space. Frames play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and probability. In this paper, we introduce the concepts of operator frame for the space $End_{mathcal{A}}^{ast}(mathcal{H})$ of all adjointable operators on a Hilbert $mathcal{A}$-module $mathcal{H}$ and establish some results.Keywords: Frame, operator frame, $C^{ast}$-algebra, Hilbert $mathcal{A}$-modules
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Pages 97-104In this paper, we present the generalized hyperstability results of cubic functional equation in ultrametric Banach spaces using the fixed point method.Keywords: Stability, hyperstability, ultrametric space, cubic functional equation
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Pages 105-115We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of the tensor products of the representations of $B_3$. As for the tensor products of the representations of $B_4$, we only find sufficient conditions for the irreducibility of the tensor product.Keywords: Braid group, irreducible
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Pages 117-126In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions. Finally, some numerical examples are given to demonstrate the behavior of the proposed method and to support the theoretical results of this paper.Keywords: Coupled matrix equations, Frobenius norm, relaxation parameters, gradient algorithm
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Pages 127-131In this study, we investigate topological properties of fuzzy strong b-metric spaces defined in [13]. Firstly, we prove Baire's theorem for these spaces. Then we define the product of two fuzzy strong b-metric spaces defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are complete fuzzy strong b-metric spaces. Finally it is proven that a subspace of a separable fuzzy strong b-metric space is separable.Keywords: Fuzzy strong b-metric space, strong b-metric space, complete, separable
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Pages 133-143In this paper we consider the minimization of a positive semidefinite quadratic form, having a singular corresponding matrix $H$. We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method. Given this approach and based on the strong duality principle, we provide a closed formula for the calculation of the Lagrange multipliers $\lambda$ in the cases when (i) the constraint equation is consistent and (ii) the constraint equation is inconsistent, using the general normal equation. In both cases the Moore-Penrose inverse will be used to determine a unique solution of the problems. In addition, in the case of a consistent constraint equation, we also give sufficient conditions for our solution to exist using the well known KKT conditions.Keywords: Moore-Penrose inverse, general normal equation, constrained optimization, Lagrange multipliers, duality principle, KKT conditions
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Pages 145-158In this paper, first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points. Finally, as consequences of these theorems, we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. We present an example to illustrate the usability of these theorems.Keywords: (α, Θ)−ω-contractions, Best proximity point, 1, 2−modular metric space