International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 447-450

On isomorphisms and hyper-reflexivity of closed subspace lattices

Han Deguang

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.


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 is a hyper-reflexive subspace lattice, then ϕT(){H} is hyper-reflexive where ϕT is a homomorphism induced by T.