Spectral Theory and Applications of Linear Operators and Block Operator Matrices

2015 ◽  
Author(s):  
Aref Jeribi
Keyword(s):  
Spectral Theory ◽  
Linear Operators ◽  
Operator Matrices ◽  
Block Operator ◽  
Block Operator Matrices

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.

Sharp Inequalities for the Numerical Radii of Block Operator Matrices

2019 ◽  
Vol 45 (4) ◽  
pp. 687-703
Author(s):  
M. Ghaderi Aghideh ◽  
M. S. Moslehian ◽  
J. Rooin
Keyword(s):  
Operator Matrices ◽  
Block Operator ◽  
Block Operator Matrices

Variational principles for eigenvalues of block operator matrices

2002 ◽  
Vol 51 (6) ◽  
pp. 1427-1460 ◽  
Author(s):  
H. Langer ◽  
M. Langer ◽  
Christiane Tretter
Keyword(s):  
Variational Principles ◽  
Operator Matrices ◽  
Block Operator ◽  
Block Operator Matrices

scholarly journals Essential numerical ranges for linear operator pencils

2019 ◽  
Vol 40 (4) ◽  
pp. 2256-2308
Author(s):  
Sabine Bögli ◽  
Marco Marletta
Keyword(s):  
Linear Operator ◽  
Numerical Range ◽  
Projection Methods ◽  
Operator Pencil ◽  
Operator Matrices ◽  
New Concepts ◽  
Block Operator ◽  
Block Operator Matrices ◽  
Spectral Pollution ◽  
Operator Pencils

Abstract We introduce concepts of essential numerical range for the linear operator pencil $\lambda \mapsto A-\lambda B$. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor even connected. The new concepts allow us to describe the set of spectral pollution when approximating the operator pencil by projection and truncation methods. Moreover, by transforming the operator eigenvalue problem $Tx=\lambda x$ into the pencil problem $BTx=\lambda Bx$ for suitable choices of $B$, we can obtain nonconvex spectral enclosures for $T$ and, in the study of truncation and projection methods, confine spectral pollution to smaller sets than with hitherto known concepts. We apply the results to various block operator matrices. In particular, Theorem 4.12 presents substantial improvements over previously known results for Dirac operators while Theorem 4.5 excludes spectral pollution for a class of nonselfadjoint Schrödinger operators which has not been possible to treat with existing methods.

On the group invertibility of operators

2016 ◽  
Vol 31 ◽  
pp. 492-510
Author(s):  
Chunyuan Deng
Keyword(s):  
Hilbert Spaces ◽  
Main Topic ◽  
Reverse Order ◽  
Operator Matrices ◽  
Reverse Order Law ◽  
Block Operator ◽  
Block Operator Matrices ◽  
Group Inverses ◽  
Triangular Block ◽  
Equivalent Conditions

The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.

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