International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 447-450
doi:10.1155/S0161171291000601

On isomorphisms and hyper-reflexivity of closed subspace lattices

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(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.