scholarly journals Approximation of the block numerical range of block operator matrices

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3877-3881
Author(s):  
Jiahui Yu ◽  
Alatancang Chen ◽  
Junjie Huang ◽  
Jiaojiao Wu
Keyword(s):  
Numerical Range ◽  
Projection Methods ◽  
Operator Matrices ◽  
Block Operator ◽  
Block Operator Matrices

In this paper we obtain an approximation of the block numerical range of bounded and unbounded block operator matrices by projection methods.

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.

Geometric of numerical and quadratic numerical range for block operator matrices

2021 ◽  
Author(s):  
Amer M. Salman ◽  
Ahmad Izani Md Ismail ◽  
Maisarah Haji Mohd ◽  
Ahmed Muhammad
Keyword(s):  
Numerical Range ◽  
Operator Matrices ◽  
Block Operator ◽  
Block Operator Matrices

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
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