Hilbert lattices with the extension property
type: Item
instance of: scholarly article
title: Hilbert lattices with the extension property
zbMATH Open document ID: 0672.06005
DOI: 10.1007/BF00182116
author: Herbert Gross
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: The author proves that there exist Hilbert lattices L with the property (extension) that each ortho-isomorphism \(\tau\) : [0,a]\(\to [0,b]\) between arbitrary interval sublattices of height at least 3 in the orthocomplemented lattice L can be extended to an ortho-automorphism of L. These examples of lattices with the extension property are of infinite height. On the level of sesquilinear spaces the extension property is of interest because this property implies orthomodularity of the underlying polarity lattice of orthoclosed subspaces. The author also constructs Hilbert lattices that do not have the extension property but do enjoy the cancellation property.
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 4099384
zbMATH Keywords: Hilbert lattices
zbMATH Keywords: ortho-isomorphism
zbMATH Keywords: interval sublattices
zbMATH Keywords: orthocomplemented lattice
zbMATH Keywords: extension
zbMATH Keywords: sesquilinear spaces
zbMATH Keywords: orthomodularity
zbMATH Keywords: polarity lattice of orthoclosed subspaces
zbMATH Keywords: cancellation property
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4099384