The Finsler geometry of certain covering groups of operator groups
type: Item
instance of: scholarly article
title: The Finsler geometry of certain covering groups of operator groups
zbMATH Open document ID: 0674.58005
author: S. H. Smith
published in: Hokkaido Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: In J. Aust. Math. Soc. 42, 196-222 (1987; Zbl 0614.58007), the author has investigated the Finsler geometry - in a natural Finsler structure - of both the full and the Fredholm unitary, orthogonal, and symplectic groups of a Hilbert space. In this sequel he considers similar questions for the associated non-trivial covering groups, namely the Fredholm spinor group and the coverings of the Fredholm unitary group. There is no evident relation between the global Finsler geometry of a covering group and that of the original group, unless one remains sufficiently close to the identity, and the author presents some unexpected results, e.g. that the universal cover of the Fredholm unitary group is bounded if and only if the underlying Hilbert space is of infinite dimension.
Mathematics Subject Classification ID: 58B99
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 4104021
zbMATH Keywords: Finsler geometry
zbMATH Keywords: symplectic groups
zbMATH Keywords: Fredholm spinor group
zbMATH Keywords: Fredholm unitary group
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381517780
OpenAlex ID: W2042687875
DOI: 10.14492/HOKMJ/1381517780
description: scientific article; zbMATH DE number 4104021