On linear maps preserving generalized invertibility and related properties

Let H be an infinite-dimensional complex Hilbert space, B ( H ) be the algebra of all bounded linear operators on H. We study surjective linear maps on B ( H ) preserving generalized invertibility. We also investigate surjective linear maps preserving Fredholm (respectively, semi-Fredholm) operators...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-09, Vol.345 (1), p.20-25
Main Authors: Boudi, Nadia, Hadder, Youness
Format: Article
Language:English
Subjects:
Closed range
Exact sciences and technology
Functional analysis
Generalized inverse
Hilbert space
Jordan homomorphism
Linear preserver problems
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Semi-Fredholm operators
Several complex variables and analytic spaces
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Summary:Let H be an infinite-dimensional complex Hilbert space, B ( H ) be the algebra of all bounded linear operators on H. We study surjective linear maps on B ( H ) preserving generalized invertibility. We also investigate surjective linear maps preserving Fredholm (respectively, semi-Fredholm) operators. Our results improve those of Mbekhta, Rodman and Šemrl.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.03.066