Title

Additive Derivations Of Certain Reflexive Algebras

Keywords

Additive derivations; Quasi-spatiality; Reflexive algebras; script J sign-subspace lattices

Abstract

Let ℒ be a script J sign-subspace lattice on a Banach space X, Algℒ be the associated reflexive algebra and A be a subalgebra of AlgLscr; containing all finite rank operators in Algℒ. If either dimK = ∞ or dimK-⊥ = ∞ for every K ∈ ℒ with K ≠ (0) and K- ≠ X, then every additive derivation D from A into Algℒ is linear and quasi-spatial, that is, there exists a densely defined, closed linear operator T: Dom(T) ⊆ X → X with its domain Dom(T) invariant under every element of A, such that D(A)x = (TA -AT)x for all A ∈ A and x ∈ Dom(T). This result can apply to those reflexive algebras with atomic Boolean subspace lattices and pentagon subspace lattices, respectively. © 2006 University of Houston.

Publication Date

8-17-2006

Publication Title

Houston Journal of Mathematics

Volume

32

Issue

2

Number of Pages

521-530

Document Type

Article

Personal Identifier

scopus

Socpus ID

33747032885 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33747032885

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