scholarly journals Operator Hyperreflexivity of Subspace Lattices

2010 ◽  
Vol 68 (3) ◽  
pp. 383-390
Author(s):  
J. Bračič ◽  
K. Kliś-Garlicka ◽  
V. Müller ◽  
I. G. Todorov
Keyword(s):  
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.

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.

scholarly journals Automorphic images of commutative subspace lattices

1986 ◽  
Vol 296 (1) ◽  
pp. 217-217 ◽  
Author(s):  
K. J. Harrison ◽  
W. E. Longstaff
Keyword(s):  
Subspace Lattices

scholarly journals On two questions of Halmos concerning subspace lattices

1979 ◽  
Vol 75 (1) ◽  
pp. 85-85 ◽  
Author(s):  
W. E. Longstaff ◽  
Peter Rosenthal
Keyword(s):  
Subspace Lattices
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