We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the basic separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly,...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Let H be a complex Hilbert space. We study the geometry of the space of pairs (A,E), for A a (semidefinite bounded linear) positive operator on H and E a (bounded linear) projection on H such that AE = E∗A. Departamento de Matemática, Facultad de Ingenieŕıa,UBA, Buenos Aires(C1063ACV), Argentina; Instituto Argentino de Matemática CONICET, Saavedra 15, Buenos Aires (1083), Argentina. E-mail addr...

In this paper, we consider the optimal disturbance rejection problem for (possibly infinite dimensional) linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, whic...

Given bounded linear operators T1, T2 and T3, this paper investigates certain invariance properties of the operator product T1XT3 with respect to the choice of bounded linear operator X, where X is a generalized inverse of T2. Different types of generalized inverses are taken into account.