When are full represenations of algebras of operators on Banach spaces automatically faithful?

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00523863" target="_blank" >RIV/67985840:_____/20:00523863 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/sm181116-30-5" target="_blank" >http://dx.doi.org/10.4064/sm181116-30-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm181116-30-5" target="_blank" >10.4064/sm181116-30-5</a>

Result language
angličtina
Original language name
When are full represenations of algebras of operators on Banach spaces automatically faithful?
Original language description
We examine when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we show that for certain Banach spaces X the following property holds: For every non-zero Banach space Y every surjective algebra homomorphism ψ:B(X)→B(Y) is automatically injective. In the second part we consider the question in the opposite direction: Building on the work of Kania, Koszmider, and Laustsen [Trans. London Math. Soc., 2014] we show that for every separable, reflexive Banach space X there is a Banach space YX and a surjective but not injective algebra homomorphism ψ:B(YX)→B(X).
Czech name
—
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
—
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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