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

 

Stability of the surjectivity
of endomorphisms and isometries of $\mathcal{B}(H)$


Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 126 (1998), 853-861
MSC (1991): Primary 47B49, 47D25, 46L40
MathSciNet review: 1423322
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Abstract: We determine the largest positive number $c$ with the property that whenever $\Phi,\Psi$ are endomorphisms, respectively unital isometries of the algebra of all bounded linear operators acting on a separable Hilbert space, $\| \Phi(A)-\Psi (A)\|<c\| A\|$ holds for every nonzero $A$ and $\Phi$ is surjective, then so is $\Psi$. It turns out that in the first case we have $c=1$, while in the second one $c=2$.


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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O.Box 12, Hungary
Email: molnarl@math.klte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04130-6
PII: S 0002-9939(98)04130-6
Keywords: Endomorphisms, isometries, operator algebras, Jordan *-homomorphisms
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: September 10, 1996
Additional Notes: Research partially supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T–016846 F–019322 and by MHB Bank, "A Magyar Tudományért" Foundation.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society