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

 

An elementary proof for a characterization of *-isomorphisms


Authors: S. H. Kulkarni, M. T. Nair and M. N. N. Namboodiri
Journal: Proc. Amer. Math. Soc. 134 (2006), 229-234
MSC (2000): Primary 47L10; Secondary 47L30
Published electronically: June 13, 2005
MathSciNet review: 2170562
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07973-6
PII: S 0002-9939(05)07973-6
Keywords: *-isomorphism, unitary operator, orthogonal projection
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.