Complemented subspaces of spaces of multilinear forms and tensor products, II. Noncommutative Lp spaces

FINITE DIMENSIONAL SUBSPACES OF NONCOMMUTATIVE Lp Spaces

We prove the following noncommutative version of Lewis’s classical result. Every n-dimensional subspace E of Lp(M) (1 < p < ∞) for a von Neumann algebra M satisfies dcb(E,RC n p ) ≤ cp · n ̨̨ ̨ 1 2 − 1 p ̨̨ ̨ for some constant cp depending only on p, where 1 p + 1 p = 1 and RC p = [Rn∩ Cn, Rn +Cn] 1 p . Moreover, there is a projection P : Lp(M) → Lp(M) onto E with ‖P‖cb ≤ cp · n ̨̨ ̨ 1 2 − 1 p ̨̨ ̨ . We fo...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Noncommutative Lp spaces, Operator spaces and Applications

Overview of the field. NoncommutativeLp-spaces are at the heart of this conference. These spaces have a long history going back to pioneering works by von Neumann, Dixmier and Segal. They are the analogues of the classical Lebesgue spaces of pintegrable functions, where now functions are replaced by operators. These spaces have been investigated for operator algebras with a trace, and then arou...

On quasi-complemented subspaces of banach spaces.

Complemented Subspaces of Spaces Obtained by Interpolation

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0, A1) such that A0 and A1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, hav...