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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000601 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |