Perturbations of surjective homomorphisms between algebras of operators on Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00550976" target="_blank" >RIV/67985840:_____/22:00550976 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/15666" target="_blank" >https://doi.org/10.1090/proc/15666</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/15666" target="_blank" >10.1090/proc/15666</a>

Result language
angličtina
Original language name
Perturbations of surjective homomorphisms between algebras of operators on Banach spaces
Original language description
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 φ, ψ are endomorphisms of B(H) such that φ(A) − ψ(A) < A and ψ is surjective, then so is φ. The aim of this paper is to extend this result to a larger class of Banach spaces including p and Lp spaces, where 1 < p < ∞. En route to the proof we show that for any Banach space X from the above class all faithful, unital, separable, reflexive representations of B(X) which preserve rank one operators are in fact isomorphisms.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Linear-analysis techniques in operator algebras and vice versa</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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