Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $c=2$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B49, 47D25, 46L40

Retrieve articles in all journals with MSC (1991): 47B49, 47D25, 46L40

Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O.Box 12, Hungary

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia