Non-Operator Reflexive Subspace Lattices

2008 ◽  
Vol 62 (4) ◽  
pp. 595-599 ◽  
Author(s):  
Kamila Kliś-Garlicka ◽  
Vladimir Müller
Keyword(s):  
Reflexive Subspace ◽  
Subspace Lattices

The Tensor Product Formula for Reflexive Subspace Lattices

1995 ◽  
Vol 38 (3) ◽  
pp. 308-316 ◽  
Author(s):  
K. J. Harrison
Keyword(s):  
Tensor Product ◽  
Operator Algebra ◽  
Product Formula ◽  
Completely Distributive ◽  
Reflexive Subspace ◽  
Complemented Lattice ◽  
Csl Algebra ◽  
Subspace Lattices

AbstractWe give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.

Structure in Reflexive Subspace Lattices

1982 ◽  
Vol s2-26 (1) ◽  
pp. 117-131 ◽  
Author(s):  
Frank Gilfeather ◽  
David R. Larson
Keyword(s):  
Reflexive Subspace ◽  
Subspace Lattices

scholarly journals Tensor products of reflexive subspace lattices.

1984 ◽  
Vol 31 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Alan Hopenwasser
Keyword(s):  
Tensor Products ◽  
Reflexive Subspace ◽  
Subspace Lattices

scholarly journals On isomorphisms and hyper-reflexivity of closed subspace lattices

1991 ◽  
Vol 14 (3) ◽  
pp. 447-450
Author(s):  
Han Deguang
Keyword(s):  
Hilbert Spaces ◽  
Closed Subspace ◽  
Short Paper ◽  
Subspace Lattice ◽  
Reflexive Subspace ◽  
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 ofξ(H1)onξ(H2). We also proved that ifTis inL(H)such that0∈¯π(T)andℱis a hyper-reflexive subspace lattice, thenϕT(ℱ)∪{H}is hyper-reflexive whereϕTis a homomorphism induced byT.

scholarly journals Representations and operations on reflexive subspace lattices

2012 ◽  
Vol 42 (4) ◽  
pp. 321-328 ◽  
Author(s):  
Wei YUAN ◽  
ChengJun HOU ◽  
GuangFeng CHEN ◽  
AiJu DONG
Keyword(s):  
Reflexive Subspace ◽  
Subspace Lattices

scholarly journals Derivations, local derivations and atomic boolean subspace lattices

2002 ◽  
Vol 66 (3) ◽  
pp. 477-486 ◽  
Author(s):  
Pengtong Li ◽  
Jipu Ma
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Linear Operator ◽  
Subspace Lattice ◽  
Local Derivation ◽  
Densely Defined ◽  
Subspace Lattices

Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.

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