Related papers: P-Operators on Hilbert Spaces

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…

A matrix is called a P-matrix if all its principal minors are positive. P-matrices have found important applications in functional analysis, mathematical programming, and dynamical systems theory. We introduce a new class of real matrices…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

A complex number $\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\B$ if there exists a non-zero bounded linear operator $X$ acting on $\B$ such that $XT=\lambda TX$. We show that there are…

Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.

In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal…

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

Given a positive operator-valued measure $\nu$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert…

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results…

Each bounded operator T on an infinite dimensional Hilbert space H is a sum of three operators that are similar to positive operators; two such operators are sufficient if T is not a compact perturbation of a scalar. The spectra of L\"uders…

Real linear operators between two complex Banach spaces unify naturally two important classes of linear operators and antilinear operators. We give a survey of basic geometric, spectral and duality properties of real linear operators. The…

This paper extends the notion of a p-hyponormal operator for a bounded right linear quaternionic operator defined on a right quaternionic Hilbert space. Several fundamental properties of complex p-hyponormal operators are investigated for…

In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space, and consider the class of (left or right) Schur multipliers that can be approached in the multiplier…

A commuting triple of Hilbert space operators $(A,S,P)$ is said to be a \textit{$\mathbb{P}$-contraction} if the closed pentablock $\overline{\mathbb P}$ is a spectral set for $(A,S,P)$, where \[ \mathbb{P}:=\left\{(a_{21}, \mbox{tr}(A_0),…

In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a…

A bounded linear operator $A$ on a Hilbert space $\mathcal{H}$ is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. We show that if $A$ is posinormal with closed range, then $A^n$ is posinormal and has closed…

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by $\Sigma$, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new…

It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…