Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Jordan and Lie derivations of $φ$-Johnson amenable Banach algebras

Hoger Ghahramani, Parvin Zamani

Abstract

Let U be a $φ$-Johnson amenable Banach algebra in which $φ$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a.x=φ(a)x$ for all a in U and x in X or $x.a=φ(a)x$ for all a in U and x in X. We show that every continuous Jordan derivation from U to X is a derivation, and every continuous Lie derivation from U to X decomposed into the sum of a continuous derivation and a continuous center-valued trace.

Jordan and Lie derivations of $φ$-Johnson amenable Banach algebras

Abstract

Let U be a -Johnson amenable Banach algebra in which is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that for all a in U and x in X or for all a in U and x in X. We show that every continuous Jordan derivation from U to X is a derivation, and every continuous Lie derivation from U to X decomposed into the sum of a continuous derivation and a continuous center-valued trace.

Paper Structure

This paper contains 5 sections, 10 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Some useful technical results
  4. Jordan derivations
  5. Lie derivations

Key Result

Theorem 3.1

Let $\mathfrak{U}$ be a Banach algebra and $\phi \in \Delta (\mathfrak{U} )$. The following are equivalent.

Theorems & Definitions (17)

  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Theorem 4.1
  • proof
  • Corollary 4.2
  • Corollary 4.3
  • ...and 7 more