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Symmetric bi-derivations on certain Banach algebras

M. Eisaei, Gh. R. Moghimi

Abstract

Let $A$ be a Banach algebra with a right identity $u$ such that $uA$ is commutative and semisimple. In this paper, we investigate symmetric bi-derivations of $A$ and detremine their range. We also study symmetric bi-derivations of $A$ with their $k$-centralizing trace. Finally, we prove every symmetric Jordan bi-derivation of $A$ is a symmetric bi-derivation.

Symmetric bi-derivations on certain Banach algebras

Abstract

Let be a Banach algebra with a right identity such that is commutative and semisimple. In this paper, we investigate symmetric bi-derivations of and detremine their range. We also study symmetric bi-derivations of with their -centralizing trace. Finally, we prove every symmetric Jordan bi-derivation of is a symmetric bi-derivation.
Paper Structure (2 sections, 4 theorems, 30 equations)

This paper contains 2 sections, 4 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Main Results

Key Result

Theorem 2.1

Let $D: A \times A \rightarrow A$ be a symmetric bi-derivation. Then the range of $D$ is contained into $\emph{ran}(A)$.

Theorems & Definitions (9)

  • Theorem 2.1
  • proof
  • Remark 2.2
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof
  • Corollary 2.5
  • Example 2.6