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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary proof for a characterization of *-isomorphisms
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by S. H. Kulkarni, M. T. Nair and M. N. N. Namboodiri
Proc. Amer. Math. Soc. 134 (2006), 229-234
DOI: https://doi.org/10.1090/S0002-9939-05-07973-6
Published electronically: June 13, 2005

Abstract:

We give an elementary proof of a result which characterizes onto *-isomorphisms of the algebra $BL(H)$ of all the bounded linear operators on a Hilbert space $H$. A known proof of this result (Arveson, 1976) relies on the theory of irreducible representations of $C^*$-algebras, whereas the proof given by us is based on elementary properties of operators on a Hilbert space which can be found in any introductory text on Functional Analysis.
References
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Bibliographic Information
  • S. H. Kulkarni
  • Affiliation: Department of Mathematics, Indian Institute of Technology - Madras, Chennai 600036, India
  • Email: shk@iitm.ac.in
  • M. T. Nair
  • Affiliation: Department of Mathematics, Indian Institute of Technology - Madras, Chennai 600036, India
  • Email: mtnair@iitm.ac.in
  • M. N. N. Namboodiri
  • Affiliation: Department of Mathematics, Cochin University of Science and Technology, Kochi-682002, India
  • Email: nambu@cusat.ac.in
  • Received by editor(s): August 12, 2004
  • Received by editor(s) in revised form: August 27, 2004
  • Published electronically: June 13, 2005
  • Communicated by: Joseph A. Ball
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 229-234
  • MSC (2000): Primary 47L10; Secondary 47L30
  • DOI: https://doi.org/10.1090/S0002-9939-05-07973-6
  • MathSciNet review: 2170562