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A REMARK ON CONTRACTIBLE BANACH ALGEBRAS OF OPERATORS.

A REMARK ON CONTRACTIBLE BANACH ALGEBRAS OF OPERATORS.

Authors :
SADR, MAYSAM MAYSAMI
Source :
Mathematical Reports; 2024, Vol. 26 Issue 3/4, p207-218, 12p
Publication Year :
2024

Abstract

For a Banach algebra A, we say that an element M in A ⊗<superscript>γ</superscript> A is a hypercommutator if (a ⊗ 1)M = M(1 ⊗ a) for every a ∈ A. A diagonal for a Banach algebra is a hyper-commutator whose image under diagonal mapping is 1. It is well known that a Banach algebra is contractible iff it has a diagonal. The main aim of this note is to show that for any Banach subalgebra A ⊆ L(X) of bounded linear operators on infinite-dimensional Banach space X, which contains the ideal of finite-rank operators, the image of any hyper-commutator of A under the canonical algebra-morphism L(X) ⊗<superscript>γ</superscript> L(X) → L(X ⊗<superscript>γ</superscript> X), vanishes. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
15823067
Volume :
26
Issue :
3/4
Database :
Complementary Index
Journal :
Mathematical Reports
Publication Type :
Academic Journal
Accession number :
181745903
Full Text :
https://doi.org/10.59277/mrar.2024.26.76.3.4.207