Banach spaces with trivial isometries
type: Item
instance of: scholarly article
title: Banach spaces with trivial isometries
zbMATH Open document ID: 0619.46012
DOI: 10.1007/BF02776242
author: Steven F. Bellenot
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A Banach space is said to have trivial isometries if the only (onto) isometries are plus or minus the identity. (Hence we are considering Banach spaces over the reals.) We show each separable Banach space has an equivalent norm with only trivial isometries. Also an equivalent norm on a non-separable Hilbert space with only trivial isometries is constructed. The constructions are based on ''pimples'', a way of decreasing the norm so that the unit ball has two ''cones'' added.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 4004903
zbMATH Keywords: Banach spaces with trivial isometries
zbMATH Keywords: local uniform convexity
zbMATH Keywords: extreme points
zbMATH Keywords: equivalent norm
zbMATH Keywords: pimples
zbMATH Keywords: cones
MaRDI profile type: Publication
cites work: Q4734306
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cites work: Geometry of Banach spaces. Selected topics
cites work: Q4136031
description: scientific article; zbMATH DE number 4004903