Related papers: Properties of operator systems, corresponding to c…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…

In this paper, the notion of operator means in the setting of JB-algebras is introduced and their properties are studied. Many identities and inequalities are established, most of them have origins from operators on Hilbert space but they…

In this paper, we present controlled finite continuous frames in a finite dimensional Hilbert space and we study some properties of them. Parseval controlled integral frames are presented and we characterize operators that construct…

It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently…

General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…

A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.

For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…

It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hilbert space to a rigged Hilbert space. In this note, we…

Given an infinite graph $G$ on countably many vertices, and a closed, infinite set $\Lambda$ of real numbers, we prove the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $\Lambda$.

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…

This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…

In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a…

In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…

The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…

We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum of a bounded operator on a bi complex Hilbert space is…

We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on…