International Journal of Nonlinear Analysis and Applications

Integration as a generalization of the integral operator

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Birjand, Birjand, Iran

2 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad

Abstract

Let A be an algebra. A \textit{derivation} on A is a linear mapping δ:A→A such that δ(ab)=δ(a)b+aδ(b) for every a,b∈A. As a dual to this notion, we consider a linear mapping Δ:A→A with the property Δ(a)Δ(b)=Δ(Δ(a)b+aΔ(b)) for every a,b∈A and we call it an \textit{integration}. In this paper, we give some examples, counterexamples and facts concerning integrations on algebras. Furthermore, we state and prove a characterization for integrations on finite dimensional matrix algebras.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 273-280
  • Receive Date: 01 June 2021
  • Revise Date: 30 March 2022
  • Accept Date: 08 April 2022