Operator spaces and similarity problems.
Operator spaces which are one-sided M-ideals in their bidual
We generalize an important class of Banach spaces, the M-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M-embedded operator spaces are the operator spaces which are one-sided M-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon-Nikodým property and many more, are retained in the non-commutative setting. We also discuss the dual...
Operatorenalgebren mit einer endlichen Anzahl von maximalen Idealen
Operators acting on certain Banach spaces of analytic functions.
Operators Factoring through Banach Lattices and Ideal Norms
A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.
Operators in finite distributive subspace lattices II
In a previous paper we gave an example of a finite distributive subspace lattice ℒ on a Hilbert space and a rank two operator of Algℒ that cannot be written as a finite sum of rank one operators from Algℒ. The lattice ℒ was a specific realization of the free distributive lattice on three generators. In the present paper, which is a sequel to the aforementioned one, we study Algℒ for the general free distributive lattice with three generators (on a normed space). Necessary and sufficient conditions...
Operators which respect norm intervals
Operators with extension property and the principle of local reflexivity
Order theory and interpolation in operator algebras
In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator...
Partial *-algebras of closed operators and their commutants. I. General structure
Partial *-algebras of closed operators and their commutants. II. Commutants and bicommutants
Periodic Schrödinger Operators with (Non-Periodic) Magnetic and Electric Potentials.
Perturbation of a Fredholm complex by inessential operators.
Perturbation of the spectrum οf an essentially selfadjoint operator
The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.
Perturbation of Toeplitz operators and reflexivity
It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.
Polynomial identification in uniform and operator algebras.
Pontryagin duality for convergence groups of unimodular continuous functions
Positive linear maps of matrix algebras
A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.
Powers and Logarithms
There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers...
p-representable operators in Banach spaces.