Derivations, local and 2-local derivations of standard operator algebras
Functional Analysis
2022-03-11 v1 Operator Algebras
Abstract
Let X be a Banach space over field F (R or C). Denote by B(X) the set of all bounded linear operators on X and by F(X) the set of all finite rank operators on X. A subalgebra A of B(X) is called a standard operator algebra if A contain F(X). We give a brief proof of a well-known result that every derivation from A into B(X) is inner. There is another classical result that every local derivation on B(X) is a derivation. We extend the result by proving that every local derivation from A into B(X) is a derivation. Based on these two results, we prove that every 2-local derivation from A into B(X) is a derivation.
Keywords
Cite
@article{arxiv.2203.05268,
title = {Derivations, local and 2-local derivations of standard operator algebras},
author = {Jun He and Haixia Zhao and Guangyu An},
journal= {arXiv preprint arXiv:2203.05268},
year = {2022}
}