Relations for the spectrum of a 3 × 3 block operator matrix

2020 ◽  
Vol 2020 (2) ◽  
pp. 134-144
Author(s):  
Z.E. Mustafoeva ◽  
T.H. Rasulov
Keyword(s):  
Operator Matrix ◽  
Block Operator Matrix ◽  
Block Operator

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg’s model type

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Afif Amar ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Operator Matrix ◽  
Model Type ◽  
Block Operator Matrix ◽  
Growing Cell ◽  
Block Operator ◽  
Abstract Boundary

AbstractIn this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberg’s model type, this last arises in growing cell populations. The entries of block operator matrix associated to this system are nonlinear and act on the Banach space X p:= L p([0, 1] × [a, b]; dµ dv), where 0 ≤ a < b < ∞; 1 < p < ∞.

scholarly journals The p-Drazin inverse for operator matrix over Banach algebras

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4597-4605
Author(s):  
Huanyin Chen ◽  
Honglin Zou ◽  
Tugce Calci ◽  
Handan Kose
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Block Operator Matrix ◽  
Block Operator

An element a in a Banach algebra A has p-Drazin inverse provided that there exists b ? comm(a) such that b = b2a,ak-ak+1b?J(A) for some k ? N. In this paper, we present new conditions for a block operator matrix to have p-Drazin inverse. As applications, we prove the p-Drazin invertibility of the block operator matrix under certain spectral conditions.

scholarly journals Perturbation theory, M-essential spectra of operator matrices

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1187-1196
Author(s):  
Boulbeba Abdelmoumen ◽  
Sonia Yengui
Keyword(s):  
Banach Space ◽  
Perturbation Theory ◽  
Banach Spaces ◽  
General Class ◽  
Operator Matrix ◽  
Operator Matrices ◽  
Essential Spectra ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Block Operator Matrices

In this paper, we will establish some results on perturbation theory of block operator matrices acting on Xn, where X is a Banach space. These results are exploited to investigate the M-essential spectra of a general class of operators defined by a 3x3 block operator matrix acting on a product of Banach spaces X3.

scholarly journals On the mixed-type generalized inverses of the products of two operators

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4361-4376
Author(s):  
Rufang Liu ◽  
Haiyan Zhang ◽  
Chunyuan Deng
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Generalized Inverses ◽  
Operator Matrix ◽  
Closed Range ◽  
Matrix Methods ◽  
Block Operator Matrix ◽  
Inclusion Relations ◽  
Block Operator ◽  
Necessary And Sufficient

Let A, B and be closed range operators. The explicit matrix expressions for various generalized inverses are obtained by using block operator matrix methods. Some subtle relationships between the properties of sub-blocks in operator matrices A, B and their range relations are built. New necessary and sufficient conditions for the equivalent relations, inclusion relations and mixed-type generalized inverses relations are presented. Some recent mixed-type reverse-order laws results are covered and many new mixed-type generalized inverses relations are established by using this block-operator matrix technique.

scholarly journals J-Self-Adjoint Projections in Krein Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiao-Ming Xu ◽  
Yile Zhao
Keyword(s):  
Matrix Representation ◽  
Krein Space ◽  
Operator Matrix ◽  
Matrix Representations ◽  
Isotropic Part ◽  
Fundamental Symmetry ◽  
Block Operator Matrix ◽  
Krein Spaces ◽  
Regular Subspace ◽  
Block Operator

Let ℋ be a Krein space with fundamental symmetry J. Starting with a canonical block-operator matrix representation of J, we study the regular subspaces of ℋ. We also present block-operator matrix representations of the J-self-adjoint projections for the regular subspaces of ℋ, as well as for the regular complements of the isotropic part in a pseudo-regular subspace of ℋ.

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