Stability of the surjectivity of endomorphisms and isometries of $\mathcal {B}(H)$
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- by Lajos Molnár PDF
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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 $c=2$.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 853-861
- MSC (1991): Primary 47B49, 47D25, 46L40
- DOI: https://doi.org/10.1090/S0002-9939-98-04130-6
- MathSciNet review: 1423322