Numerical range of operators acting on Banach spaces |
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| Authors: | Khadijeh Jahedi Bahmann Yousefi |
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| Institution: | 1. Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
2. Department of Mathematics, Payame Noor University, P.O. Box: 19395-3697, Tehran, Iran
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| 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. |
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