In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. These are norms obtained from the projective norm by some natural operations. We prove that there are exactly six ...

The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in a symmetrically-normed ideal J contained in B(H) defined by a symmetric norming function (s.n.f.). The norms considered ...

We introduce the symmetric-Radon-Nikodým property (sRN pr operty) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective ...

We give the symmetric version of five lemmas which are essential for the theory of tensor products (and norms). These are: the approximation, extension, embedding, density and local technique lemma. Some applications of ...

We use the Aron–Berner extension to prove that the set of extreme points of the unit ball of the space of integral k-homogeneous polynomials over a real Banach space X is {±φk: φ ∈ X∗, φ = 1}. With this description we ...

Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has ...

Let I I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H H . Let View the MathML source {pi}w1 (1≤w≤∞) (1≤w≤∞) be a family of mutually orthogonal projections on H H . The ...

We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional ...

Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multilinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions ...