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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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000601 |
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| _version_ | 1832555049226600448 |
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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. |
| format | Article |
| id | doaj-art-5c590aa4cdc846298669c4d6724f714d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |