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Perturbations of surjective homomorphisms between algebras of operators on Banach spaces.
- Source :
-
Proceedings of the American Mathematical Society . Feb2022, Vol. 150 Issue 2, p747-761. 15p. - Publication Year :
- 2022
-
Abstract
- A remarkable result of Molnár [Proc. Amer. Math. Soc. 126 (1998), pp. 853–861] states that automorphisms of the algebra of operators acting on a separable Hilbert space are stable under "small" perturbations. More precisely, if \phi,\psi are endomorphisms of \mathcal {B}(\mathcal {H}) such that \|\phi (A)-\psi (A)\|<\|A\| and \psi is surjective, then so is \phi. The aim of this paper is to extend this result to a larger class of Banach spaces including \ell _p and L_p spaces, where 1<p<\infty. En route to the proof we show that for any Banach space X from the above class all faithful, unital, separable, reflexive representations of \mathcal {B} (X) which preserve rank one operators are in fact isomorphisms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 150
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 154272924
- Full Text :
- https://doi.org/10.1090/proc/15666