Related papers: A Characterization of $(\sigma,\tau)-$ derivations…

Let $\mathcal{H}$ be a complex Hilbert space, $\mathcal{B(H)}$ be the algebra of all bounded linear operators on $\mathcal{H}$ and $\mathcal{A} \subseteq \mathcal{B(H)}$ be a von Neumann algebra without central summands of type $I_1$. For…

Let $(M,\tau,\sigma,\Gamma)$ be a (finite) von Neumann dynamical system and let $N$ be a $\Gamma$-invariant unital von Neumann subalgebra of $M$. If $V\subset L^2(M)$ is a right $N$-submodule whose projection $p_V$ has finite trace in $<…

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves…

For a ring $R$ with an automorphism $\sigma$, an $n$-additive mapping $\Delta:R\times R\times... \times R \rightarrow R$ is called a skew $n$-derivation with respect to $\sigma$ if it is always a $\sigma$-derivation of $R$ for each…

Given a von Neumann algebra $M$ we introduce so called central extension $mix(M)$ of $M$. We show that $mix(M)$ is a *-subalgebra in the algebra $LS(M)$ of all locally measurable operators with respect to $M,$ and this algebra coincides…

Let $f$ be a Lipschitz map from a subset $A$ of a stratified group to a Banach homogeneous group. We show that directional derivatives of $f$ act as homogeneous homomorphisms at density points of $A$ outside a $\sigma$-porous set. At…

Let U be a $\phi $-Johnson amenable Banach algebra in which $\phi$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a.x=\phi(a)x$ for all a in U and x in X or $x.a=\phi(a)x$ for all a in…

The derivation problem is a familiar one concerning group algebras, particularly $L_1(G)$ and von Neumann algebras. In this paper, we study the Banach bimodule $\ell_p(G)$, which is generated by the $\ell_p$ norm over a specific class of…

Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we define a subset sigma(f,p) of K, called spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in the linear…

Let $M$ be a von Neumann algebra equipped with a normal semi-finite faithful trace (nsf trace in short) and let $T\colon M\to M$ be a contraction. We say that $T$ is absolutely dilatable if there exist another von Neumann algebra $M'$…

We define $\Gamma_q(B,S \otimes H)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(\pi_j,B,A,D)$ and to a subset $1 \in S = S^* \subset A$ and, under certain assumptions, prove…

Let $\mathscr{R}$ be a finite von Neumann algebra with a faithful tracial state $\tau $ and let $\Delta$ denote the associated Fuglede-Kadison determinant. In this paper, we characterize all unital bijective maps $\phi$ on the set of…

We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph products relative to subalgebras coming from induced subgraphs.…

Let $A$ be a von Neumann algebra with no central summands of type $I_1$. We will show that every nonlinear Lie $n$-derivation on $A$ is of the standard form, i.e. it can be expressed as a sum of an additive derivation and a central-valued…

On the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q…

The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…

Let $\mathcal{X}$ be a Banach space over the complex field $\mathbb{C}$ and $\mathcal{B(X)}$ be the algebra of all bounded linear operators on $\mathcal{X}$. Let $\mathcal{N}$ be a non-trivial nest on $\mathcal{X}$, ${\rm Alg}\mathcal{N}$…

We establish, via geometric quantization of the supercotangent bundle sM of (M,g), a correspondence between its conformal geometry and those of the spinor bundle. In particular, the Kosmann Lie derivative of spinors is obtained by…

We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…