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
Department of Mathematics, Qufu Normal University, Shandong, China
Received 15 March 1988; Revised 2 January 1991
Copyright © 1991 Han Deguang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.