Exterior algebra of a Banach space
type: Item
instance of: scholarly article
title: Exterior algebra of a Banach space
zbMATH Open document ID: 1134.46047
author: W. Ramasinghe
published in: Bulletin des Sciences Mathématiques
publication date: 2007-05-04T00:00:00Z
review text: In this carefully written paper, based on results of the author's Ph.D.\ thesis, the exterior (Grassmann) algebra \(\Lambda_\ast X\) of a Banach space \(X\) is introduced and equipped with several norms, among them the projective and the injective norms \(\|\cdot \|_\wedge\) and \(\|\cdot \|_\vee\), respectively (which are related to the homonymous norms by Grothendieck). Several universal properties of these normed spaces are shown, and it turns out that \((\Lambda_\ast X)_{\wedge}\) is a Banach algebra. As explicit examples, the author shows that \((\Lambda_\ast \ell_1)_{\wedge}=\ell_1\) and \((\Lambda_\ast \ell_2)_{\wedge}\not=\ell_2\). It is also shown that the norms \(\|\cdot \|_\wedge\) and \(\|\cdot \|_\vee\) are in duality.
reviewed by: Heinz Junek
Mathematics Subject Classification ID: 46M99
zbMATH DE Number: 5149358
zbMATH Keywords: exterior algebra
zbMATH Keywords: Grassmann algebra
zbMATH Keywords: tensor norm
zbMATH Keywords: projective tensor norm
MaRDI profile type: Publication
full work available at URL: j.bulsci.2006.05.007
OpenAlex ID: W2006875919
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DOI: 10.1016/J.BULSCI.2006.05.007
description: scientific article; zbMATH DE number 5149358