Minimal and maximal operator spaces and operator systems in entanglement theory

Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory

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,...

Subspaces of Maximal Operator Spaces

A Banach space E can be embedded into B(H) in a variety of ways. The embeddings giving rise to the minimal and maximal possible operator space norms (introduced in [1], [3] and [4] and further investigated in [21] and [22]) are especially interesting to us. Let A be the set of all functionals on E of norm not exceeding 1 and let B be the set of all linear maps T : E → Mn such that ||T || ≤ 1 (h...

Operator Theory and Modulation Spaces

This is a “problems” paper. We isolate some connections between operator theory and the theory of modulation spaces that were stimulated by a question of Feichtinger’s regarding integral and pseudodifferential operators. We discuss several problems inspired by this question, and give a reformulation of the original question in operator-theoretic terms. A detailed discussion of the background an...

The " Maximal " Tensor Product of Operator Spaces

In analogy with the maximal tensor product of C *-algebras, we define the " maximal " tensor product E 1 ⊗ µ E 2 of two operator spaces E 1 and E 2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor

Operator Theory and Operator Algebras