On isomorphisms and hyper-reflexivity of closed subspace lattices

Han Deguang

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-4

Abstract:

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 ( H 1 ) on ξ ( H 2 ) . We also proved that if T is in L ( H ) such that 0 ∈ ¯ π ( T ) and ℱ is a hyper-reflexive subspace lattice, then ϕ T ( ℱ ) ∪ { H } is hyper-reflexive where ϕ T is a homomorphism induced by T .

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:387125

DOI: 10.1155/S0161171291000601

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