Intersection properties of balls in spaces of compact operators

Asvald Lima

Displaying similar documents to “Intersection properties of balls in spaces of compact operators”

On decompositions of Banach spaces into a sum of operator ranges

V. Fonf, V. Shevchik (1999)

Studia Mathematica

Similarity:

It is proved that a separable Banach space X admits a representation $X = X_{1} + X_{2}$ as a sum (not necessarily direct) of two infinite-codimensional closed subspaces $X_{1}$ and $X_{2}$ if and only if it admits a representation $X = A_{1} (Y_{1}) + A_{2} (Y_{2})$ as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation $X = T_{1} (Z_{1}) + T_{2} (Z_{2})$ such that neither of the operator ranges $T_{1} (Z_{1})$ , $T_{2} (Z_{2})$ contains an infinite-dimensional closed subspace...

Ultraproducts of $L_{1}$ -predual spaces

S. Heinrich (1981)

Fundamenta Mathematicae

Similarity:

Transitivity for linear operators on a Banach space

Bertram Yood (1999)

Studia Mathematica

Similarity:

Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if $x_{1}, \dots, x_{n}$ and $y_{1}, \dots, y_{n}$ are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that $T (x_{k}) = y_{k}$ , $k = 1, \dots, n$ . We prove that some proper multiplicative subgroups of G have this property.

For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent

Walter Schachermayer (1985)

Studia Mathematica

Similarity:

Banach spaces which are $M$ -ideals in their bidual have property $(u)$

Gilles Godefroy, D. Li (1989)

Annales de l'institut Fourier

Similarity:

We show that every Banach space which is an $M$ -ideal in its bidual has the property $(u)$ of Pelczynski. Several consequences are mentioned.

A Weierstrass-Stone theorem for Choquet simplexes

David Alan Edwards, G. F. Vincent-Smith (1968)

Annales de l'institut Fourier

Similarity:

Soit $X \neq \emptyset$ un convexe compact d’un espace localement convexe séparé, soit $A (X)$ l’espace de fonctions réelles affines continues sur $X$ , et soit $L$ un sous-espace de $A (X)$ linéaire qui contient les fonctions constantes. Parmi les faces fermées de $X$ sur lesquelles les fonctions de $L$ sont toutes constantes on appelle les faces maximales $L$ -faces. Nos théorèmes principaux donnent quelques conditions sous lesquelles $L$ contient exactement ces fonctions qui sont constantes sur chaque $L$ -face. En particulier,...

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Eve Oja, Märt Põldvere (1996)

Studia Mathematica

Similarity:

Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace...

Properly semi-L-embedded complex spaces

Angel Rodríguez Palacios (1993)

Studia Mathematica

Similarity:

We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

Similarity:

Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...