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Regularity of operators on essential extensions of the compacts

Author: Arupkumar Pal
Journal: Proc. Amer. Math. Soc. 128 (2000), 2649-2657
MSC (1991): Primary 46H25, 47C15
Published electronically: February 28, 2000
MathSciNet review: 1705741
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A semiregular operator on a Hilbert $C^*$-module, or equivalently, on the $C^*$-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian $C^*$-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed.

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Additional Information

Arupkumar Pal
Affiliation: Indian Statistical Institute, 7, SJSS Marg, New Delhi–110016, India

Keywords: Hilbert $C^*$-modules, regular operators, $C^*$-algebras, essential extensions
Received by editor(s): June 29, 1998
Received by editor(s) in revised form: October 22, 1998
Published electronically: February 28, 2000
Additional Notes: The author was partially supported by the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society