Displaying similar documents to “Quantitative unconditionality of Banach spaces E for which K(E) is an M-ideal in ℒ(E)”

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Unconditional ideals in Banach spaces

G. Godefroy, N. Kalton, P. Saphar (1993)

Studia Mathematica

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We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition X * * * = X ⊥ ⊕ X * is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel X ⊥ . We undertake a general study of h-ideals and u-ideals. For example...

Banach spaces with a supershrinking basis

Ginés López (1999)

Studia Mathematica

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We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without c 0 copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the c 0 -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in c 0 .