Let [Lambda] be a barrelled perfect (in the sense of J. Dieudonné) Köthe space of measurable functions defined on an atomless finite Radon measure space. Let X be a Banach space containing a copy of c0, then the space [Lambda(X)] of [Lambda]-Bochner integrable functions contains a complemented copy of c0.
We give sufficient conditions on Banach spaces and so that their projective tensor product , their injective tensor product , or the dual contain complemented copies of .
We prove that the direct sum and the product of countably many copies of L1[0, 1] are primary locally convex spaces. We also give some related results.
The purpose of this note is to announce, without proofs, some results concerning vector valued multilinear operators on a product of C(K) spaces.
A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely continuous...
We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.
We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from into d(w,1), where is a predual of a complex Lorentz sequence space d(w,1), if and only if wi ∈ c₀∖ℓ₂.
For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters...
We investigate the relationships between strongly extreme, complex extreme, and complex locally uniformly rotund points of the unit ball of a symmetric function space or a symmetric sequence space E, and of the unit ball of the space E(ℳ,τ) of τ-measurable operators associated to a semifinite von Neumann algebra (ℳ,τ) or of the unit ball in the unitary matrix space . We prove that strongly extreme, complex extreme, and complex locally uniformly rotund points x of the unit ball of the symmetric...
We study the Complex Unconditional Metric Approximation Property for translation invariant spaces of continuous functions on the circle group. We show that although some “tiny” (Sidon) sets do not have this property, there are “big” sets Λ for which has (ℂ-UMAP); though these sets are such that contains functions which are not continuous, we show that there is a linear invariant lifting from these spaces into the Baire class 1 functions.