Related papers: Conjugate operators for finite maximal subdiagonal…

We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly…

An operator algebra $\mathcal{A}$ acting on a Hilbert space is said to have the closability property if every densely defined linear transformation commuting with $\mathcal{A}$ is closable. In this paper we study the closability property of…

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\tau_i:X \to X$ for $1 \le i \le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra…

If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) for which $ C U…

It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is…

We transfer a large part of the circle of theorems characterizing the generalization of classical $H^\infty$ known as `weak* Dirichlet algebras', to Arveson's noncommutative setting of subalgebras of finite von Neumann algebras.

Let $\mathcal{M}$ be a separable von Neumann algebra with center $\mathcal{Z}(\mathcal{M})$. An operator $T$ in $\mathcal{M}$ is called irreducible if the von Neumann algebra $W^*(T)$ generated by $T$ has trivial relative commutant, i.e.,…

We consider an abstract sequence $\{A_n\}_{n=1}^\infty$ of closed symmetric operators on a separable Hilbert space $\mathcal{H}$. It is assumed that all $A_n$'s have equal deficiency indices $(k,k)$ and thus self-adjoint extensions…

For a von Neumann algebra M acting on a Hilbert space H with a cyclic and separating vector v, we investigate the structure of Dirichlet forms on the natural standard form associated with the pair (M,v). For a general Lindblad type…

The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…

Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators $A,B$ on a Hilbert space $H$ are unitarily equivalent modulo compacts, i.e., $uAu^*+K=B$ for some unitary $u\in \mathcal{U}(H)$ and compact self-adjoint operator $K$,…

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of…

We prove that two dual operator algebras are weak$^*$ Morita equivalent if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak$^*$-continuous on appropriate morphism…

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly…

Let $\mathcal{H}$ be a separable complex Hilbert space. A conjugate-linear map $C:\mathcal{H}\to \mathcal{H}$ is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let…

We examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains…

Let N be a nest on a Hilbert space H and AlgN the corresponding nest algebra. We obtain a characterization of the compact and weakly compact multiplication operators defined on nest algebras. This characterization leads to a description of…

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

Let $\ell^{p}$, $1\leq p<\infty$, be the Banach space of absolutely $p$-th power summable sequences and let $\pi_{n}$ be the natural projection to the $n$-th coordinate for $n\in\mathbb{N}$. Let $\mathfrak{W}=\{w_{n}\}_{n=1}^{\infty}$ be a…