Invertibility preserving linear maps and algebraic reflexivity of elementary operators of length one

Author:
Peter Semrl

Journal:
Proc. Amer. Math. Soc. **130** (2002), 769-772

MSC (2000):
Primary 47B49

DOI:
https://doi.org/10.1090/S0002-9939-01-06177-9

Published electronically:
August 29, 2001

MathSciNet review:
1866032

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Abstract | References | Similar Articles | Additional Information

Let and be real or complex Banach spaces. We show that a surjective linear map preserving invertibility in both directions is either of the form or the form , where , , , and are bounded invertible linear operators. As an application we improve a result of Larson and Sourour on algebraic reflexivity of elementary operators of length one.

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Additional Information

**Peter Semrl**

Affiliation:
Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia

Email:
peter.semrl@fmf.uni-lj.si

DOI:
https://doi.org/10.1090/S0002-9939-01-06177-9

Received by editor(s):
July 22, 1998

Received by editor(s) in revised form:
September 14, 2000

Published electronically:
August 29, 2001

Additional Notes:
This research was supported in part by a grant from the Ministry of Science of Slovenia

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society