Duality and multiplication operators |
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Authors: | Pratibha G Ghatage Shunhua Sun |
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Institution: | (1) Department of Mathematics, Cleveland State University, 44115 Cleveland, Ohio;(2) Department of Mathematics, Sichuan University, 610064 Chengdu, Peoples' Republic of China |
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Abstract: | We describe a space of functions contained inxxLx
(D)C(D G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLx
a
2
and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC
*-subalgebra ofxxLx
(D) which we conjecture to be a proper super-set ofU.Most of this research was done while the second author was visiting Cleveland State University. He would like to thank the Mathematics Department for its hospitality. He would also like to thank the NNSFC for partial support. |
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Keywords: | |
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