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$θ$-derivations on convolution algebras

M. Eisaei, Gh. R. Moghimi

Abstract

In this paper, we investigate $θ$-derivations on Banach algebra $ L_0^{\infty} (w)^*$. First, we study the range of them and prove the Singer-Wermer conjucture. We also give a characterization of the space of all $θ$-derivations on $ L_0^{\infty} (w)^*$. Then, we prove automatic continuity and Posner's theorems for $θ$-derivations.

$θ$-derivations on convolution algebras

Abstract

In this paper, we investigate -derivations on Banach algebra . First, we study the range of them and prove the Singer-Wermer conjucture. We also give a characterization of the space of all -derivations on . Then, we prove automatic continuity and Posner's theorems for -derivations.
Paper Structure (2 sections, 7 theorems, 34 equations)

This paper contains 2 sections, 7 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Main Results

Key Result

Theorem 2.1

Let $\theta$ be a homomorphism on $L_0^{\infty} (w)^*$ and $D$ be a $\theta$-derivation on $L_0^{\infty} (w)^*$. Then the following statements hold. (i)$D$ maps $\emph{ran} (L_0^{\infty} (w)^*)$ and $\Lambda (L_0^{\infty} (w)^*)$ into $\emph{ran} (L_0^{\infty} (w)^*)$. (ii) If $\theta$ is an isomorp

Theorems & Definitions (13)

  • Theorem 2.1
  • proof
  • Corollary 2.2
  • Proposition 2.3
  • proof
  • Theorem 2.4
  • proof
  • Proposition 2.5
  • proof
  • Corollary 2.6
  • ...and 3 more