An elementary proof for a characterization of *-isomorphisms
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- by S. H. Kulkarni, M. T. Nair and M. N. N. Namboodiri PDF
- Proc. Amer. Math. Soc. 134 (2006), 229-234 Request permission
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
- William Arveson, An invitation to $C^*$-algebras, Graduate Texts in Mathematics, No. 39, Springer-Verlag, New York-Heidelberg, 1976. MR 0512360, DOI 10.1007/978-1-4612-6371-5
- Balmohan V. Limaye, Functional analysis, 2nd ed., New Age International Publishers Limited, New Delhi, 1996. MR 1427262
- Angus Ellis Taylor and David C. Lay, Introduction to functional analysis, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR 564653
Additional 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