Home > Research > Publications & Outputs > Approximately multiplicative maps between algeb...

Electronic data

  • AMNM-BE_arX2

    Rights statement: First published in American Mathematical Society in volume 375, number 10, October 2022, published by the American Mathematical Society. © 2021 American Mathematical Society.

    Accepted author manuscript, 540 KB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License


Text available via DOI:

View graph of relations

Approximately multiplicative maps between algebras of bounded operators on Banach spaces

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>31/10/2022
<mark>Journal</mark>Transactions of the American Mathematical Society
Issue number10
Number of pages27
Pages (from-to)7121-7147
Publication StatusPublished
Early online date29/07/22
<mark>Original language</mark>English


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 L p[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 = ℓ 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.).