Lie centralizers at zero products on a class of operator algebras

Document Type

Article

Publication Date

4-1-2021

Abstract

Let A be an algebra. In this paper, we consider the problem of determining a linear map ? on A satisfying a, b? A, ab=0??([a,b])=[?(a),b](C1) or ab=0??([a,b])=[a,?(b)](C2). We first compare linear maps satisfying (C1) or (C2), commuting linear maps, and Lie centralizers with a variety of examples. In fact, we see that linear maps satisfying (C1), (C2) and commuting linear maps are different classes of each other. Then, we introduce a class of operator algebras on Banach spaces such that if A is in this class, then any linear map on A satisfying (C1) (or (C2)) is a commuting linear map. As an application of these results, we characterize Lie centralizers and linear maps satisfying (C1) (or (C2)) on nest algebras.

This document is currently not available here.

Share

COinS