Multilinear forms, subsymmetric polynomials, and spreading models on Banach spaces
type: Item
instance of: scholarly article
title: Multilinear forms, subsymmetric polynomials, and spreading models on Banach spaces
zbMATH Open document ID: 0872.46012
author: Raquel Gonzalo
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-12T00:00:00Z
review text: A sequence \(\{x_k\}_1^\infty\) in a Banach space \(X\) is said to have a lower \(q\)-estimate \((1<q<\infty)\) if \(|\sum_1^n a_kx_k|\geq C(\sum_{k=1}^n|a_k|^q)^{1/q}\) for a fixed \(C>0\) and for all \(n\in\mathbb{N}\) and arbitrary scalars \(a_k\). Relations between lower \(q\)-estimates and polynomials behaviour are considered. For example: if in \(X\) there is no weakly null normalized sequence with a lower \(q\)-estimate, then every polynomial of degree less than \(q\) on \(X\) is weakly sequentially continuous. Approximation on subspaces of homogeneous polynomials by subsymmetric ones is studied. Applications to algebras generated by polynomials on \(X\) are given.
reviewed by: M. I. Kadets
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B28
zbMATH DE Number: 930197
zbMATH Keywords: multilinear form
zbMATH Keywords: subsymmetric polynomial
zbMATH Keywords: lower \(q\)-estimate
zbMATH Keywords: weakly null normalized sequence
zbMATH Keywords: algebras generated by polynomials
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0322
OpenAlex ID: W2057067018
DOI: 10.1006/JMAA.1996.0322
description: scientific article; zbMATH DE number 930197