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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularity of operators on essential extensions of the compacts
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by Arupkumar Pal PDF
Proc. Amer. Math. Soc. 128 (2000), 2649-2657 Request permission

Abstract:

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–110 016, India
  • Email: arup@isid.ac.in
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 2649-2657
  • MSC (1991): Primary 46H25, 47C15
  • DOI: https://doi.org/10.1090/S0002-9939-00-05611-2
  • MathSciNet review: 1705741