On isomorphisms and hyper-reflexivity of closed subspace lattices

There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ξ(H1) on ξ(H2). We also p...

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Main Author: Han Deguang
Format: Article
Language:English
Published: Wiley 1991-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171291000601
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author Han Deguang
author_facet Han Deguang
author_sort Han Deguang
collection DOAJ
description There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ξ(H1) on ξ(H2). We also proved that if T is in L(H) such that 0∈¯π(T) and ℱ is a hyper-reflexive subspace lattice, then ϕT(ℱ)∪{H} is hyper-reflexive where ϕT is a homomorphism induced by T.
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issn 0161-1712
1687-0425
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publishDate 1991-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-5c590aa4cdc846298669c4d6724f714d2025-02-03T05:49:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114344745010.1155/S0161171291000601On isomorphisms and hyper-reflexivity of closed subspace latticesHan Deguang0Department of Mathematics, Qufu Normal University, Shandong, ChinaThere are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ξ(H1) on ξ(H2). We also proved that if T is in L(H) such that 0∈¯π(T) and ℱ is a hyper-reflexive subspace lattice, then ϕT(ℱ)∪{H} is hyper-reflexive where ϕT is a homomorphism induced by T.http://dx.doi.org/10.1155/S0161171291000601reflexivityhyper-reflexivityisomorphism.
spellingShingle Han Deguang
On isomorphisms and hyper-reflexivity of closed subspace lattices
International Journal of Mathematics and Mathematical Sciences
reflexivity
hyper-reflexivity
isomorphism.
title On isomorphisms and hyper-reflexivity of closed subspace lattices
title_full On isomorphisms and hyper-reflexivity of closed subspace lattices
title_fullStr On isomorphisms and hyper-reflexivity of closed subspace lattices
title_full_unstemmed On isomorphisms and hyper-reflexivity of closed subspace lattices
title_short On isomorphisms and hyper-reflexivity of closed subspace lattices
title_sort on isomorphisms and hyper reflexivity of closed subspace lattices
topic reflexivity
hyper-reflexivity
isomorphism.
url http://dx.doi.org/10.1155/S0161171291000601
work_keys_str_mv AT handeguang onisomorphismsandhyperreflexivityofclosedsubspacelattices