arXiv subjects

M. Eisaei

Publications and source records attributed to M. Eisaei.

6 recordsLinked to original sources

arXiv2025

Jordan Left $\alpha$-centralizers on Algebras with Applications to Group Algebras

We prove that every Jordan left $\alpha$-centralizer from an algebra $A$ with a right identity into an arbitrary algebra $B$ is a left $\alpha$-centralizer. This implies all Jordan homomorphisms between such algebras are homomorphisms. We extend this result to continuous Jordan left $\alpha$-centralizers when $A$ has a bounded left approximate identity. For the group algebra $L^1(G)$, we characterize weakly compact Jordan left $\alpha$-centralizers when $\alpha$ is continuous and surjective, showing $L^1(G)$ admits a weakly compact epimorphism if and only if $G$ is finite. Consequently, the existence of a non-zero $\alpha$-derivation on $L^1(G)$ is equivalent to $G$ being compact and non-abelian.

math.FA↗

arXiv2024

Jordan left $α$-centralizer on certain algebras

In this paper, we investigate Jordan left $α$-centralizer on algebras. We show that every Jordan left $α$-centralizer on an algebra with a right identity is a left $α$-centralizer. We also investigate this result for Banach algebras with a bounded approximate identity. Finally, we study Jordan left $α$-centralizer on group algebra $L^1(G)$.

math.FA↗

arXiv2024

On $θ$-centralizing $θ$-generalized derivations on convolution algebras

Let $θ$ be an isomorphism on $L_0^{\infty} (w)^*$. In this paper, we investigate $θ$-generalized derivations on $L_0^{\infty} (w)^*$. We show that every $θ$-centralizing $θ$-generalized derivation on $L_0^{\infty} (w)^*$ is a $θ$-right centralizer. We also prove that this result is true for $θ$-skew centralizing $θ$-generalized derivations.

math.FA↗

arXiv2024

$θ$-derivations on convolution algebras

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.

math.FA↗

arXiv2024

Left $θ$-derivations on weighted convolution algebras

Let $θ$ be a homomorphism on $L_0^\infty({\Bbb R}^+, ω)^*$. In this paper, we study left $θ$-derivations on $L_0^\infty({\Bbb R}^+, ω)^*$. We show that every left $θ$-derivation on $L_0^\infty({\Bbb R}^+, ω)^*$ is always a $θ$-derivation, and if $θ$ is isomorphism, then $L_0^\infty({\Bbb R}^+, ω)^*$ has no non-zero left $θ$-derivation. We also investigate automatic continuity, Singer-Wermer's conjecture and Posner's first theorem for left $θ-$derivations on $L_0^\infty({\Bbb R}^+, ω)^*$.

math.FA↗

arXiv2024

Symmetric bi-derivations on certain Banach algebras

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.

math.FA↗