Approximately multiplicative maps between algebras of bounded operators on Banach spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00562013" target="_blank" >RIV/67985840:_____/22:00562013 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/tran/8687" target="_blank" >https://doi.org/10.1090/tran/8687</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/8687" target="_blank" >10.1090/tran/8687</a>
Alternative languages
Result language
angličtina
Original language name
Approximately multiplicative maps between algebras of bounded operators on Banach spaces
Original language description
We show that for any separable reflexive Banach space X and a large class of Banach spaces E, including those with a subsymmetric shrinking basis but also all spaces Lp[0, 1] for 1 ≤ p ≤ ∞, every bounded linear map B(E) → B(X) which is approximately multiplicative is necessarily close in the operator norm to some bounded homomorphism B(E) → B(X). That is, the pair (B(E), B(X)) has the AMNM property in the sense of Johnson [J. London Math. Soc. (2) 37 (1988), pp. 294–316]. Previously this was only known for E = X = p with 1 < p < ∞, even for those cases, we improve on the previous methods and obtain better constants in various estimates. A crucial role in our approach is played by a new result, motivated by cohomological techniques, which establishes AMNM properties relative to an amenable subalgebra, this generalizes a theorem of Johnson (op cit.).
Czech name
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Czech description
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Classification
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
Result continuities
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
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
American Mathematical Society. Transactions
ISSN
0002-9947
e-ISSN
1088-6850
Volume of the periodical
375
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
7121-7147
UT code for WoS article
000834952900001
EID of the result in the Scopus database
2-s2.0-85139550910