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A Note on Weighted Composition Operators on the Fock Space

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【作者】 Feng Li-xiaZhao Lian-kuoJi You-qing

【Author】 Feng Li-xia;Zhao Lian-kuo;Ji You-qing;School of Mathematics and Computer Science, Shanxi Normal University;

【机构】 School of Mathematics and Computer Science, Shanxi Normal University

【摘要】 Based on a new characterization of bounded and compact weighted composition operators on the Fock space obtained by Le T(Le T. Normal and isometric weighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46: 847–856), this paper shows that a bounded weighted composition operator on the Fock space is a Fredholm operator if and only if it is an invertible operator, and if and only if it is a nonzero constant multiple of a unitary operator. The result is very different from the corresponding results on the Hardy space and the Bergman space.

【基金】 The NSF(11201274 and 11471189) of China
  • 【DOI】10.13447/j.1674-5647.2015.03.11
  • 【分类号】O177
  • 【被引频次】1
  • 【下载频次】26
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