On a formula of le Merdy for the complex interpolation of tensor products.
On a result of J. Johnson
On Banach spaces X such that L(Lp,X) = K(Lp,X).
On bounded approximation properties of Banach spaces
This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?
On certain subsets of Bochner integrable function spaces.
One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively.On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general theory of Banach spaces. Their structure is so...
On complementably universal Banach spaces
On complemented copies of in spaces of operators, II
We show that as soon as embeds complementably into the space of all weakly compact operators from to , then it must live either in or in .
On copies of in the bounded linear operator space
In this note we study some properties concerning certain copies of the classic Banach space in the Banach space of all bounded linear operators between a normed space and a Banach space equipped with the norm of the uniform convergence of operators.
On multilinear mappings of nuclear type.
The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.
On nicely smooth Banach spaces.
On some matrix Inequalities in Banach Spaces
On subspaces of Banach spaces where every functional has a unique norm-preserving extension
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 K(E,F)...
On subspaces of L1 which embed into ...1.
On the compact approximation property
We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net of compact operators on X such that and in the strong operator topology. Similar results for dual spaces are also proved.
On the Dunford-Pettis property of tensor product spaces
We give sufficient conditions on Banach spaces E and F so that their projective tensor product and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is completely...
On the equality between some classes of operators on Banach lattices
We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
On the geometry of and .
On the norm of a projection onto the space of compact operators
Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than max|B| + c....
On the projection constants of some topological spaces and some applications.
On the structure of derivations on certain nonamenable nuclear Banach algebras.