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Numerical range of operators acting on Banach spaces

Khadijeh Jahedi, Bahmann Yousefi (2012)

Czechoslovak Mathematical Journal

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...

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