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Articles

Certain nontrivially essentially self-adjoint weighted composition operators on H2 and

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Pages 1626-1635 | Received 14 Nov 2012, Accepted 26 Nov 2013, Published online: 28 Jan 2014
 

Abstract

In this paper, we characterize nontrivially essentially self-adjoint weighted composition operators on the Hardy space and the weighted Bergman spaces , when is not an automorphism and is continuous at . Moreover, we show that weighted composition operators on and are not nontrivially essentially self-adjoint, whenever and for .

AMS Subject Classifications:

Acknowledgments

The authors appreciate Prof. B.D. MacCluer for her attention and development of Proposition 3.1.

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