Numerical range of operators acting on Banach spaces

Khadijeh Jahedi; Bahmann Yousefi

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 2, page 495-503
  • ISSN: 0011-4642

Abstract

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The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.

How to cite

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Jahedi, Khadijeh, and Yousefi, Bahmann. "Numerical range of operators acting on Banach spaces." Czechoslovak Mathematical Journal 62.2 (2012): 495-503. <http://eudml.org/doc/247152>.

@article{Jahedi2012,
abstract = {The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.},
author = {Jahedi, Khadijeh, Yousefi, Bahmann},
journal = {Czechoslovak Mathematical Journal},
keywords = {numerical range; weighted Hardy space; compact operator; composition operator; numerical range; weighted Hardy space; compact operator; composition operator},
language = {eng},
number = {2},
pages = {495-503},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical range of operators acting on Banach spaces},
url = {http://eudml.org/doc/247152},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Jahedi, Khadijeh
AU - Yousefi, Bahmann
TI - Numerical range of operators acting on Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 495
EP - 503
AB - The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.
LA - eng
KW - numerical range; weighted Hardy space; compact operator; composition operator; numerical range; weighted Hardy space; compact operator; composition operator
UR - http://eudml.org/doc/247152
ER -

References

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