Operator space and operator system analogs of Kirchberg's nuclear embedding theorem

Operator space embedding of Lq into Lp

The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...

OPERATOR SPACE Lp EMBEDDING THEORY I

Let X 1 and X 2 be subspaces of quotients of R ⊕ OH and C ⊕ OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X 1 ⊗ h X 2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓq (equipped with...

An Operator Embedding Theorem for Complexity Classes of Recursive Functions

NONCOMMUTATIVE L p - SPACE AND OPERATOR SYSTEM

We show that noncommutative Lp-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant 2 1 p . Therefore, noncommutative Lpspaces can be embedded into BpHq 2 1 p -completely isomorphically and complete order isomorphically. 1. Introducton A unital involutive subspace of BpHq had been abstractly characterized by Choi and Effros [CE]. Their axioms are based on obse...

An Operator Corona Theorem

In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...