Related papers: Commutator estimates in $W^*$-factors

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…

Whether an almost-commuting pair of operators must be close to a commuting pair is a central question in operator and matrix theory. We investigate this problem for pairs of $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of…

This paper is devoted to derivations on the algebra $S(M)$ of all measurable operators affiliated with a finite von Neumann algebra $M.$ We prove that if $M$ is a finite von Neumann algebra with a faithful normal semi-finite trace $\tau$,…

We investigate when a map on a selfadjoint operator space $E$ is an embedding, i.e., when its unitisation in the sense of Werner is completely isometric. Combining with results of Russell, of Ng, and of Dessi, the second and the last…

The hermitian indices of a selfadjoint operator $C$ on a Kre\u{i}n space $\mathcal H$ are defined as geometric measures of positivity and negativity of the operator. A different pair of indices arises in the Bogn\'ar-Kr\'amli factorization…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…

Let $W$ be a finite reflection group. For a given $w \in W$, the following assertion may or may not be satisfied: (*) The principal Bruhat order ideal of $w$ contains as many elements as there are regions in the inversion hyperplane…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

Let $T:X\to X$ be a linear power bounded operator on Banach space. Let $X_0$ is a subspace of vectors tending to zero under iterating of $T$. We prove that if $X_0$ is not equal to $X$ then there exists $\lambda$ in Sp(T) such that, for…

The Laplacian $\Delta_{\mathbb{S}^{n-1}}$ on the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ has the property that it can explicitly be expressed in terms of $\Lambda$, the Dirichlet-to-Neumann map of the unit ball, as…

A W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. This paper concentrates on the study of 1-dimensional representations of these algebras. Under some conditions on a nilpotent element…

We consider a four-dimensional globally hyperbolic spacetime $(M,g)$ conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of…

We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…

For a unital $C^*$-algebra $\mathcal A$ and a subspace $\mathcal B$ of $\mathcal A$, a characterization for a best approximation to an element of $\mathcal A$ in $\mathcal B$ is obtained. As an application, a formula for the distance of an…

Let $M$, $N$, $R$ be $W^{*}$--algebras, with $R$ unitally embedded in both $M$ and $N$. by using Reduction Theory, we extend the previous description of the $W^{*}$--tensor product $M\bar\otimes_{R}N$ over the common $W^{*}$--subalgebra $R$…

Given $\beta\in\mathbb{Z}[i]$ with $|\beta|>1$ and a finite set $D\subset\mathbb{Q}(i)$, let \[K_{\beta, D}=\left\{\sum_{j=1}^{\infty}\frac{d_j}{\beta^j}: d_j\in D, \forall j\geq 1\right\}.\] Let $\mathcal{S}$ be a finite set of…

Let $\mathcal{A}$ be a unital algebra, $\delta$ be a linear mapping from $\mathcal{A}$ into itself and $m$, $n$ be fixed integers. We call $\delta$ an (\textit{m, n})-derivable mapping at $Z$, if…

The main result concerns a sigma-unital C*-algebra A, a strongly lower semicontinuous element h of A**, the enveloping von Neumann algebra, and the set of self-adjoint elements a of A such that a \le h - delta 1 for some delta > 0, where 1…

Given any irreducible inclusion $\mB \subset \mA$ of unital $C^*$-algebras with a finite-index conditional expectation $E: \mA \to \mB$, we show that the set of $E$-compatible intermediate $C^*$-subalgebras is finite, thereby generalizing a…