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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on density for the core of unbounded Bergman operators


Authors: Sherwin Kouchekian and James E. Thomson
Journal: Proc. Amer. Math. Soc. 139 (2011), 2067-2072
MSC (2010): Primary 32A36; Secondary 47B38, 32A35
Published electronically: November 5, 2010
MathSciNet review: 2775384
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Abstract: In this paper, we identify a large collection of open subsets of the complex plane for which the core of corresponding unbounded Bergman operators is densely defined. This result gives the necessary background to investigate the concept of invariant subspaces, index, and cyclicity in the unbounded case.


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Additional Information

Sherwin Kouchekian
Affiliation: Department of Mathematics & Statistics, University of South Florida, Tampa, Florida 33620-5700
Email: skouchekian@usf.edu

James E. Thomson
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: jthomson@math.vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10608-1
PII: S 0002-9939(2010)10608-1
Keywords: Unbounded Bergman operators, functional calculus, core of a Bergman operator
Received by editor(s): November 4, 2009
Received by editor(s) in revised form: May 31, 2010
Published electronically: November 5, 2010
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.