Actions that characterize \(l_\infty^{(n)}\)
type: Item
instance of: scholarly article
title: Actions that characterize \(l_\infty^{(n)}\)
zbMATH Open document ID: 0898.46011
DOI: 10.1016/S0024-3795(97)00233-4
published in: Linear Algebra and its Applications
publication date: 1998-11-02T00:00:00Z
review text: It is a classical result of Nachbin that if the identity operator on an \(n\)-dimensional Banach space \(V\) can be extended to any Banach space with the same norm, then \(V\) is isometric to \(\ell^{(n)}_\infty\). In this work, the authors show that the identity is the only linear operator with this property.
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 1109498
author: B. L. Chalmers
author: Boris Shekhtman
reviewed by: Ioana Ciorănescu
MaRDI profile type: Publication
cites work: A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces
cites work: Extension constants of unconditional two-dimensional operators
cites work: Q4885493
cites work: Q4885494
cites work: On the extension of operators with a finite-dimensional range
cites work: A Theorem of the Hahn-Banach Type for Linear Transformations
cites work: Q4041061
full work available at URL: s0024-3795(97)00233-4
OpenAlex ID: W2094519259
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description: scientific article; zbMATH DE number 1109498