Jordan derivations on the $\theta-$Lau products of Banach algebras

TL;DR

This paper investigates Jordan derivation-like maps on the $ heta$-Lau products of Banach algebras, characterizing their structure and conditions under which they become derivation-like, including their centralizing properties.

Contribution

It provides a characterization of Jordan derivation-like maps on $ heta$-Lau products and establishes conditions for these maps to be derivation-like, extending understanding of algebraic structures.

Findings

Jordan derivation-like maps are characterized on $ heta$-Lau products.

Under certain conditions, these maps are shown to be derivation-like.

The centralizing property of these maps is analyzed.

Abstract

In this paper, we study Jordan derivation-like maps on the $\theta-$Lau products of algebras. We characterize them and prove that under certain condition any Jordan derivation-like maps on the $\theta-$Lau products is a derivation-like map. Moreover, we investigate the concept of centralizing for Jordan derivation-like maps on the $\theta-$Lau products of algebras.