Stability of the surjectivity

of endomorphisms and isometries of

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 with the property that whenever are endomorphisms, respectively unital isometries of the algebra of all bounded linear operators acting on a separable Hilbert space, holds for every nonzero and is surjective, then so is . It turns out that in the first case we have , while in the second one .

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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

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