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The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures

P. G. CasazzaN. J. Nielsen — 2003

Studia Mathematica

The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently B ( , X * ) = Π ( , X * ) . If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach...

Rosenthal operator spaces

M. JungeN. J. NielsenT. Oikhberg — 2008

Studia Mathematica

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L p -space, then it is either an L p -space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non-Hilbertian complemented operator subspaces of non-commutative L p -spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every 2 < p < ∞ which can be considered...

Unsolved Problems

1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

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