Composition operators on a Banach space of analytic functions |
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| Authors: | Cao Guangfu N Elias P Ghatage Yu Dahai |
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| Institution: | (1) Department of Mathematics, Sichuan University, 610064 Chengdu, China;(2) 6611 Tauglewood Court 3B, 46323 Hammond, IN;(3) Department of Mathematics, Cleveland State University, 44115 Cleveland, OH;(4) Department of Mathematics, Sichuan University, 610063 Chengdu, China |
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| Abstract: | In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 |
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| Keywords: | Bergman space Composition operator Compact operator Fredholm operator |
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