Shapiroʼs Theorem for subspaces

A Bollobás-type theorem for affine subspaces

ROSENTHAL’S THEOREM FOR SUBSPACES OF NONCOMMUTATIVE Lp

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p > 1. This is a noncommutative version of Rosenthal’s result for commutative Lp spaces. Similarly for 1 ≤ q < 2, an infinite dimensional subspace X of a noncommutative Lq space either contains lq or embeds in Lp for some q < p < 2. The novelty in the noncommutative setting i...

A Reflexivity Theorem for Weakly Closed Subspaces of Operators

It was proved in [4] that the ultraweakly closed algebras generated by certain contractions on Hubert space have a remarkable property. This property, in conjunction with the fact that these algebras are isomorphic to Hx, was used in [3] to show that such ultraweakly closed algebras are reflexive. In the present paper we prove an analogous result that does not require isomorphism with Hx, and a...

Frameness bound for frame of subspaces

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

An operator corona theorem for a class of subspaces of H

Let E, E∗ be separable Hilbert spaces. If S is an open subset of T, then AS(L (E, E∗)) denotes the space of all functions f : D ∪ S → L (E, E∗) that are holomorphic in D, and bounded and continuous on D ∪ S. In this article we prove the following main results: 1. A theorem concerning the approximation of f ∈ AS(L (E, E∗)) by a function F that is holomorphic in a neighbourhood of D∪S and such th...