We give an explicit computation of the Banach envelope for the Paley-Wiener type spaces E, 0 < p < 1. This answers a question by Joel Shapiro.

Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson’s inequalities hold in these spaces.

We identify the generalised modulation spaces associated with tensor products of amalgam having a large class Banach as their local component. As consequences main results, we describe various $$L^p$$ spaces.

We study property (T) and the fixed point property for actions on L p and other Banach spaces. We show that property (T) holds when L 2 is replaced by L p (and even a subspace/quotient of L p), and that in fact it is independent of 1 ≤ p < ∞. We show that the fixed point property for L p follows from property (T) when 1 < p < 2 + ε. For simple Lie groups and their lattices, we prove that the fi...

Pietsch [5] introduced the concept of absolutely summing operators in Banach spaces and later in [6] extended this concept to absolutely p-summing operators. At the background of these concepts are the sequence spaces I p and their duality theory. The object of the present paper is to extend the above concept to abstract sequence spaces 2. The sequence spaces 2 involved are described in Section...

In this paper, we study the following operator equation: p ∈ Ax + Cx in a Banach space X , where A : D(A) ⊆ X → 2X is an accretive mapping, C : D(C) ⊆ X → X is a nonlinear mapping and p ∈ X . Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition. © 2004 Elsevier Ltd. All rights reserved.

We introduce U DS p-property (resp. U DT q-property) in Banach lattices as the property that every normalized disjoint sequence has a subse-quence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lat...

Every isometric property of Banach spaces preserved by real or complex interpolation is subspace-hereditary, and every isomorphic property of separable Banach spaces so preserved is quotient-hereditary. Introduction Many properties of Banach spaces are known to pass to interpolation spaces obtained from the real k-method of interpolation or from the complex method, completeness itself being the...