Some properties of the Pisier-Zu interpolation spaces

A. Sersouri

Displaying similar documents to “Some properties of the Pisier-Zu interpolation spaces”

Isomorphism of certain weak $L^{p}$ spaces

Denny Leung (1993)

Studia Mathematica

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It is shown that the weak $L^{p}$ spaces $ℓ^{p, \infty}, L^{p, \infty} [0, 1]$ , and $L^{p, \infty} [0, \infty)$ are isomorphic as Banach spaces.

A multidimensional Wolff theorem

Fernando Cobos, Jaak Peetre (1989)

Studia Mathematica

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The Lions's problem for Gustavsson-Peetre functor.

E.I. Bereznoi, Mieczyslaw Mastylo (1990)

Publicacions Matemàtiques

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The problem of coincidence of the interpolation spaces obtained by use of the interpolation method of Gustavsson-Peetre generated by (parameters) quasi-concave functions is investigated. It is shown that a restriction of this method to the class of all non-trivial Banach couples gives different interpolation spaces whenever two different parameters satisfying some conditions are used.

A counterexample to several questions about Banach spaces

James Halger (1977)

Studia Mathematica

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On bounded biorthogonal systems in some function spaces

A. Pličko (1986)

Studia Mathematica

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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 $c_{0}$ .

L-summands in their biduals have Pełczyński's property (V*)

Hermann Pfitzner (1993)

Studia Mathematica

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Banach spaces which are L-summands in their biduals - for example $l^{1}$ , the predual of any von Neumann algebra, or the dual of the disc algebra - have Pełczyński’s property (V*), which means that, roughly speaking, the space in question is either reflexive or is weakly sequentially complete and contains many complemented copies of $l^{1}$ .

Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic

A. Pełczyński (1971)

Studia Mathematica

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Characterizations of elements of a double dual Banach space and their canonical reproductions

Vassiliki Farmaki (1993)

Studia Mathematica

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For every element x** in the double dual of a separable Banach space X there exists the sequence $(x^{(2 n)})$ of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class $B_{1} (X) ╲ B_{1 / 2} (X)$ (resp. to the class $B_{1 / 4} (X)$ ) as the elements with the sequence $(x^{(2 n)})$ equivalent to the usual basis of $ℓ^{1}$ (resp. as the elements with the sequence $(x^{(4 n - 2)} - x^{(4 n)})$ equivalent to the...

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.

Sequence spaces and interpolation problems for analytic functions

A. Snyder (1971)

Studia Mathematica

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The $l_{1}^{n}$ problem and degrees of non-reflexivity (II)

W. Davis, J. Lindenstrauss (1976)

Studia Mathematica

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