Related papers: Compact multiplication operators on nest algebras

Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\cal P}_{\leq N}$ denote the additive group of polynomials $P\in\mathbb{Z}[x]$ with ${\rm deg}\, P\leq N$ and $P(0)=0$. Given a unitary operator $U$…

We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and…

Muthukumar and Ponnusamy \cite{MP-Tp-spaces} studied the multiplication operators on $\mathbb{T}_p$ spaces. In this article, we mainly consider multiplication operators between $\mathbb{T}_p$ and $\mathbb{T}_q$ ($p\neq q$). In particular,…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

We show, by means of a class of examples, that if $K_1$ and $K_2$ are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal,…

A multiplicative Hankel operator is an operator with matrix representation $M(\alpha) = \{\alpha(nm)\}_{n,m=1}^\infty$, where $\alpha$ is the generating sequence of $M(\alpha)$. Let $\mathcal{M}$ and $\mathcal{M}_0$ denote the spaces of…

We classify operator systems $S\subseteq \mathcal B(H)$ that act on finite dimensional Hilbert spaces by making use of the noncommutative Choquet boundary. S is said to be {\em reduced} when its boundary ideal is 0. In the category of…

We show that in the space of nuclear operators from $\ell^q(\Lambda)$ to $\ell^p(J)$ the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures. As a consequence the same is proved…

Let $T$ be a bounded linear operator on a Hilbert space. Then the Aluthge transform $\Delta T$ and the sequence $(\Delta^nT)$ of Aluthge iterates of $T$ are defined by \begin{align*} \Delta…

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…

Let $K$ be an absolutely convex infinite-dimensional compact in a Banach space $\mathcal{X}$. The set of all bounded linear operators $T$ on $\mathcal{X}$ satisfying $TK\supset K$ is denoted by $G(K)$. Our starting point is the study of the…

We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we…

We give a short proof of the nuclearity property of a class of Cuntz-Pimsner algebras associated with a Hilbert A-bimodule M, where A is a separable and nuclear C*-algebra. We assume that the left A-action on the bimodule M is given in…

In the present paper, we introduce and investigate the multiplicative order compact operators from vector lattices to $l$-algebras. A linear operator $T$ from a vector lattice $X$ to an $l$-algebra $E$ is said to be $\mathbb{omo}$-compact…

Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification…

Criteria for an algebraic operator $T$ on a complex Hilbert space $\mathcal{H}$ to be unitary are established. The main one is written in terms of the convergence of sequences of the form $\{\|T^nh\|\}_{n=0}^{\infty}$ with $h\in…

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…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the…

The authors Matsaev and Mogulskii singled out a wide class of weak perturbation of a positive compact operator $H$, of the form $H(I+S)$, where $S$ is such a compact operator that $I+S$ is continuously invertible, which does not have a…