Let H1 and H2 be indefinite inner product spaces. Let L (H1) and L (H2) be the sets of all linear operators on H1 and H2, respectively. The following result is proved: If Φ is [*]-isomorphism from L (H1) onto L (H2) then there exists U : H1 → H2 such that Φ (T) = c U T U[*] for all T ∈ L (H1) with U U[*] = c I2, U[*] U = c I1 and c = ± 1. Here I1 and I2 denote the identity maps on H1 and H2, respectively. © 2006 Elsevier Inc. All rights reserved.

K C Sivakumar

Department of Mathematics

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IIT Madras

Journal of Mathematical Analysis and Applications

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 Hubert 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. © 2005 American Mathematical Society.

Journal	Journal of Mathematical Analysis and Applications
ISSN	0022247X
Open Access	Yes