Related papers: Half-centered Operators

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…

This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a…

Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some…

An operator $T$ acting on a separable complex Hilbert space $H$ is said to be hypercyclic if there exists $f\in H$ such that the orbit $\{T^n f:\ n\in \mathbb{N}\}$ is dense in $H$. Godefroy and Shapiro \cite{GoSha} characterized those…

We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…

It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\half\mu^2x^2-\lambda x^4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C…

The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any…

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…

In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…

Let $H_1$ and $H_2$ be complex Hilbert spaces and $T:H_1\rightarrow H_2$ be a bounded linear operator. We say $T$ to be norm attaining, if there exists $x\in H_1$ with $\|x\|=1$ such that $\|Tx\|=\|T\|$. If for every closed subspace $M$ of…

Let T be a quasidiagonal operator on a separable Hilbert space. Then T is the norm limit of operators, each of which generate a finite dimensional C*-algebra, if and only if the C*-algebra generated by T is exact.

An n-tuple (n \geq 2), T = (T_1, \ldots, T_n), of commuting bounded linear operators on a Hilbert space \mathcal{H} is doubly commuting if T_i T_j^* = T_j^* T_i for all $1 \leq i < j \leq n$. If in addition, each T_i \in C_{\cdot 0}, then…

Let $n$ be any natural number. The $n$-centered operator is introduced for adjointable operators on Hilbert $C^*$-modules. Based on the characterizations of the polar decomposition for the product of two adjointable operators, $n$-centered…

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially…

This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…

In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from…

Given an arbitrary sequence of elements $\xi=\{\xi_n\}_{n\in \mathbb{N}}$ of a Hilbert space $(\mathcal{H},\langle\cdot,\cdot\rangle)$, the operator $T_\xi$ is defined as the operator associated to the sesquilinear form $…

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…