相关论文: Weak-local derivations and homomorphisms on C*-alg…

We prove that any derivation of the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a properly infinite von Neumann algebra $\mathcal{M}$ is continuous with respect to the local measure topology…

We prove that every weak-local triple derivation on a JB$^*$-triple $E$ (i.e. a linear map $T: E\to E$ such that for each $\phi \in E^*$ and each $a\in E$, there exists a triple derivation $\delta_{a,\phi} : E\to E$, depending on $\phi$ and…

In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.

The paper is devoted to local derivations on the algebra $S(\mathcal{M},\tau)$ of $\tau$-measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ and a faithful normal semi-finite trace $\tau.$ We prove that every local…

This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a…

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.

The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz…

We prove that every biorthogonality preserving linear surjection between two dual or compact C$^*$-algebras or between two von Neumann algebras is automatically continuous.

It is established that every derivation continuous with respect to the local measure topology acting on the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ is necessary…

The paper is devoted to 2-local derivations on the algebra $LS(M)$ of all locally measurable operators affiliated with a type I$_\infty$ von Neumann algebra $M.$ We prove that every 2-local derivation on $LS(M)$ is a derivation.

We prove that each local Lie $n$-derivation is a Lie $n$-derivation under mild assumptions on the unital algebras with a nontrivial idempotent. As applications, we obtain descriptions of local Lie $n$-derivations on generalized matrix…

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure…

In this article we initiate research on locally compact C*-simple groups. We first show that every C*-simple group must be totally disconnected. Then we study C*-algebras and von Neumann algebras associated with certain groups acting on…

It is proved that every 2-local derivation on an AW$^*$-algebra of type I is a derivation. Also an analog of Gleason theorem for signed measures on projections of homogenous AW$^*$-algebras except the cases of an AW$^*$-algebra of type…

In the present paper we prove that every local and $2$-local derivation on conservative algebras of $2$-dimensional algebras are derivations. Also, we prove that every local and $2$-local automorphism on conservative algebras of…

We generalize Kirchberg's weak exactness to inclusions of C*-algebras in von Neumann algebras and study some characterizations and permanence properties which are similar to those of exact groups. We then consider a similar condition to…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

We first prove that every AF-algebra is weakly central, thereby resolving a question left open by Archbold--Gogi\'c. We then establish a new characterization of weak centrality for unital $C^*$-algebras in terms of $C(X)$-algebras. The…

We prove that every {\rm(}not necessarily linear nor continuous{\rm)} 2-local triple derivation on a von Neumann algebra $M$ is a triple derivation, equivalently, the set Der$_{t} (M)$, of all triple derivations on $M,$ is algebraically…