Each operator in L (lp,lr) (1 ≤ r < p < ∞) is compact.
It is known that each bounded operator from lp → lris compact. The purpose of this paper is to present a very simple proof of this useful fact.
Eberlein compacts in
Eberlein-compacts et espaces de Radon
Edwards' separation theorem for complex Lindenstrauss spaces with application to selection and embedding Theorems.
Effective constructions of separable quotients of Banach spaces.
A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.
Eigenvalue distribution of integral operators defined by Besov-Orlicz kernels.
Eigenvalue distribution of integral operators defined by Orlicz kernels.
Éléments positifs relatifs à une algèbre hilbertienne à gauche
Embedding a topological group into its WAP-compactification
We prove that the topology of the additive group of the Banach space c₀ is not induced by weakly almost periodic functions or, what is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. We show, in contrast, that additive groups of Schwartz locally convex spaces are always representable as groups of isometries on some reflexive Banach space.
Embedding in
If is a measurable space and a Banach space, we provide sufficient conditions on and in order to guarantee that , the Banach space of all -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of if and only if does.
Embedding functions and their role in interpolation theory.
Embedding into Banach spaces with finite dimensional decompositions.
This paper deals with the following types of problems: Assume a Banach space X has some property (P). Can it be embedded into some Banach space Z with a finite dimensional decomposition having property (P), or more generally, having a property related to (P)? Secondly, given a class of Banach spaces, does there exist a Banach space in this class, or in a closely related one, which is universal for this class?
Embedding l∞N-cubes in finite-dimensional 1-subsymmetric spaces.
Embedding of presheaves into dual unit balls
Embedding sums into products of Banach spaces.
Embeddings of Besov spaces of logarithmic smoothness
This paper deals with Besov spaces of logarithmic smoothness formed by periodic functions. We study embeddings of into Lorentz-Zygmund spaces . Our techniques rely on the approximation structure of , Nikol’skiĭ type inequalities, extrapolation properties of and interpolation.
Embeddings of C(K) spaces into C(S,X) spaces with distortion strictly less than 3
In the spirit of the classical Banach-Stone theorem, we prove that if K and S are intervals of ordinals and X is a Banach space having non-trivial cotype, then the existence of an isomorphism T from C(K, X) onto C(S,X) with distortion strictly less than 3 implies that some finite topological sum of K is homeomorphic to some finite topological sum of S. Moreover, if Xⁿ contains no subspace isomorphic to for every n ∈ ℕ, then K is homeomorphic to S. In other words, we obtain a vector-valued Banach-Stone...
Embeding weakly compact sets
Endpoint estimates from restricted rearrangement inequalities.
Enflo's example of a Banach space without the approximation property