Related papers: Some examples of EP operators
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of the problem under which we can or cannot achieve different…
The Hilbert matrix $\mathcal{H}_{n,m} = (n+m+ 1)^{-1}$ has been extensively studied in previous literature. In this paper we look at generalized Hilbert operators arising from measures on the interval $[0, 1]$, such that the Hilbert matrix…
We present a new operator equality in the framework of Hilbert $C^*$-modules. As a consequence, we get an extension of the Euler--Lagrange type identity in the setting of Hilbert bundles as well as several generalized operator Bohr's…
We study nonsymmetric tridiagonal operators acting in the Hilbert space $\ell^2$ and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a…
Using Read's construction of operators without non-trivial invariant subspaces/subsets on $\ell_{1}$ or $c_{0}$, we construct examples of operators on a Hilbert space whose set of hypercyclic vectors is "large" in various senses. We give an…
The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
The main concern of this note is the Moore-Penrose inverse in the context of Banach spaces and algebras. Especially attention will be given to a particular class of elements with the aforementioned inverse, namely EP Banach space operators…
The main aim of this article is to establish several $p$-numerical radius inequalities via the $(f,g)$-Aluthge transform of Hilbert space operators and operator matrices. Furthermore, various classical numerical radius and norm inequalities…
In this note, we provide some sufficient and necessary conditions for the core inverse of the perturbed operator to have the simplest possible expression. The results improve the recent work by H. Ma (Optimal perturbation bounds for the…
In this paper, we shall give a necessary and sufficient condition for nilpotency of elementary multiplication operators and some sufficient conditions for elementary operators to be nilpotent on B(E), where E is Banach space.
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms'', i.e.\ norming an element minus a…
We present examples of non-Hausdorff, etale, essentially principal groupoids for which three results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous functions on the unit space is maximal…
We observe that for a large class of non-amenable groups $G$, one can find bounded representations of $A(G)$ on Hilbert space which are not completely bounded. We also consider restriction algebras obtained from $A(G)$, equipped with the…
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…