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 Right and Left Weyl Operator Matrices in a Banach Space Setting

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Aichun Liu ◽  
Junjie Huang ◽  
Alatancang Chen
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Operator Matrix ◽  
Weyl Operator ◽  
Operator Matrices ◽  
Space Setting ◽  
Hamiltonian Operators ◽  
Equivalent Conditions

Let X i , Y i i = 1,2 be Banach spaces. The operator matrix of the form M C = A C 0 B acting between X 1 ⊕ X 2 and Y 1 ⊕ Y 2 is investigated. By using row and column operators, equivalent conditions are obtained for M C to be left Weyl, right Weyl, and Weyl for some C ∈ ℬ X 2 , Y 1 , respectively. Based on these results, some sufficient conditions are also presented. As applications, some discussions on Hamiltonian operators are given in the context of Hilbert spaces.

scholarly journals ON THE POIN ON THE POINT SPECTRUM OF OPERA TRUM OF OPERATOR MATRIX COMIMG T X COMIMG TO A A DIAGONALIZABLE MATRIX

2019 ◽  
Vol 3 (4) ◽  
pp. 14-19
Author(s):  
Tulkin Khusenovich Rasulov ◽  
◽  
Zarina Erkin kizi Mustafoeva
Keyword(s):  
Discrete Spectrum ◽  
Hilbert Spaces ◽  
Point Spectrum ◽  
Linear Operators ◽  
Operator Matrix ◽  
Operator Matrices ◽  
Quantum Particles ◽  
Block Operator ◽  
Block Operator Matrices ◽  
Diagonalizable Matrix

It isconsidered herethediagonalizable operatormatrix . The essential and point spectrum of are described via the spectrum of the more simpler operator matrices. If the elements of a matrix are linear operators in Banach or Hilbert spaces, then it is called a block-operator matrix. One of the special classes of block operator matrices are the Hamiltonians of a system with a nonconserved number of quantum particles on an integer or noninteger lattice. The inclusion for the discrete spectrum of is established.

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.

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