The coarse Novikov conjecture and Banach spaces with Property (H)

Banach Spaces with the 2-summing Property

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar eld: the property is self-dual and any space with the property is a nite dimensional space of maximal distance to the Hilbert space of the same dimensio...

Coarse embeddability into Banach spaces

The Banach-saks Property of the Banach Product Spaces

In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.

The Complete Continuity Property in Banach Spaces

Let X be a complex Banach space. We show that the following are equivalent: (i) X has the complete continuity property, (ii) for every (or equivalently for some) 1 < p < ∞, for f ∈ h(D, X) and rn ↑ 1, the sequence frn is p-Pettis-Cauchy, where frn is defined by frn(t) = f(rne ) for t ∈ [0, 2π], (iii) for every (or equivalently for some) 1 < p < ∞, for every μ ∈ V (X), the bounded linear operato...

H-Projective Banach Spaces

and with the habitual changes in the case p = +∞. If I is a set then, l(I) denotes the Banach space L(I, ν),where ν is the counting measure. And if I is the set {1, ..., n}, the corresponding space is denoted ln . We will denote by H(X)the space of all analytic functions f : D −→ X such that ||f ||Hp(X) < +∞, with ||f ||Hp(X) = Sup {||fr||Lp(T;X) : 0 < r < 1} and fr(t) = f(rt), for all t ∈ T an...