Approximately multiplicative maps between algebras of bounded operators on Banach spaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximately multiplicative maps between algebras of bounded operators on Banach spaces

Popis výsledku v původním jazyce

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.).

Název v anglickém jazyce

Approximately multiplicative maps between algebras of bounded operators on Banach spaces

Popis výsledku anglicky

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.).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Metody lineární analýzy v operátorových algebrách a naopak</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

American Mathematical Society. Transactions

ISSN

0002-9947

e-ISSN

1088-6850

Svazek periodika

375

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

7121-7147

Kód UT WoS článku

000834952900001

EID výsledku v databázi Scopus

2-s2.0-85139550910