Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00549717" target="_blank" >RIV/67985840:_____/21:00549717 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/qmath/haaa066" target="_blank" >https://doi.org/10.1093/qmath/haaa066</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/qmath/haaa066" target="_blank" >10.1093/qmath/haaa066</a>

Result language
angličtina
Original language name
Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective
Original language description
We study automatic injectivity of surjective algebra homomorphisms from B(X)⁠, the algebra of (bounded, linear) operators on X, to B(Y)⁠, where X is one of the following long sequence spaces: c0(λ), ℓc∞(λ)⁠, and ℓp(λ) (⁠1⩽p<∞⁠) and Y is arbitrary. En route to the proof that these spaces do indeed enjoy such a property, we classify two-sided ideals of the algebra of operators of any of the aforementioned Banach spaces that are closed with respect to the ‘sequential strong operator topology’.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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