Related papers: Characterizations of all-derivable points in $B(H)…

Let $\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\in {\mathcal{A}}$ is an all-derivable point of ${\mathcal{A}}$ if every derivable linear mapping $\phi$ at $G$ (i.e. $\phi(ST)=\phi(S)T+S\phi(T)$ for any…

Suppose that $\mathscr{A}$ is an operator algebra on a Hilbert space $H$. An element $V$ in $\mathscr{A}$ is called an all-derivable point of $\mathscr{A}$ for the strong operator topology if every strong operator topology continuous…

Let $B(H)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space $H$. For $T \in B(H)$ and $\lambda \in \mathbb{C}$, let $H_{T}(\{\lambda\})$ denotes the local spectral subspace of $T$ associated…

Let $X$ be a Banach algebra and $B(X)$ be the set of all bounded linear operators on $X$. Suppose that $\alpha: B(X) \rightarrow B(X)$ is an automorphism. We say that a mapping $\delta$ from $B(X)$ into itself is derivable at $G \in B(X)$…

A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at…

The paper is devoted to 2-local derivations and 2-local automorphisms on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H.$ We prove that every 2-local derivation on $B(H)$ is a derivation. A similar result is…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

Let ${\mathcal N}$ be a nest on a complex Banach space $X$ and let $\mbox{ Alg}{\mathcal N}$ be the associated nest algebra. We say that an operator $Z\in \mbox{ Alg}{\mathcal N}$ is an all-derivable point of $\mbox{ Alg}{\mathcal N}$ if…

We present the following reflexivity-like result concerning the automorphism group of the $C^*$-algebra B(H), H being a separable Hilbert space. Let $\phi:B(H)\to B(H)$ be a multiplicative map (no linearity or continuity is assumed) which…

For a commutative C*-algebra $\mathcal A$ with unit $e$ and a Hilbert~$\mathcal A$-module $\mathcal M$, denote by End$_{\mathcal A}(\mathcal M)$ the algebra of all bounded $\mathcal A$-linear mappings on $\mathcal M$, and by…

We prove that, for every complex Hilbert space $H$, every weak-2-local derivation on $B(H)$ or on $K(H)$ is a linear derivation. We also establish that every weak-2-local derivation on an atomic von Neumann algebra or on a compact…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

We prove that, for every separable complex Hilbert space $H$, every weak-2-local $^*$-derivation on $B(H)$ is a linear $^*$-derivation. We also establish that every (non-necessarily linear nor continuous) weak-2-local derivation on a finite…

Let H and K be two Hilbert spaces and B(H) be the algebra of all bounded linear operators from H into itself. The main purpose of this paper is to obtain a characterization of bijective maps $\Phi$ : B(H) $\rightarrow$ B(K) satisfying the…

Let X be a Banach space over field F (R or C). Denote by B(X) the set of all bounded linear operators on X and by F(X) the set of all finite rank operators on X. A subalgebra A of B(X) is called a standard operator algebra if A contain…

Let $\mathcal{N}$ be a non-trivial and complete nest on a Hilbert space $H$. Suppose $d=\{d_n: n\in N\}$ is a group of linear mappings from Alg$\mathcal{N}$ into itself. We say that $d=\{d_n: n\in N\}$ is a Jordan higher derivable mapping…

Let $\mathcal{H}$ be a separable Hilbert space and $\mathcal{L}_{0}\subset B(\mathcal{H})$ a complete reflexive lattice. Let $\mathscr{K}$ be the direct sum of $n_0$ copies of $\mathcal{H}$ ($n_{0}\in\mathbb{N}$ and $n_0\geq 2$) or the…

Suppose that $\calak$ is a $C^*$-algebra acting on a Hilbert space $\calhk$, and that $\phi, \psi$ are mappings from $\calak$ into $B(\calhk)$ which are not assumed to be necessarily linear or continuous. A $(\phi, \psi)$-derivation is a…

Let $M$ be a type I von Neumann algebra with the center $Z,$ and let $LS(M)$ be the algebra of all locally measurable operators affiliated with $M.$ We prove that every $Z$-linear derivation on $LS(M)$ is inner. In particular all $Z$-linear…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…