Title
Additive derivations of certain reflexive algebras
Abbreviated Journal Title
Houst. J. Math.
Keywords
additive derivations; quasi-spatiality; reflexive algebras; J-subspace; lattices; PENTAGON SUBSPACE LATTICES; STANDARD OPERATOR-ALGEBRAS; NEST-ALGEBRAS; ISOMORPHISMS; Mathematics
Abstract
Let L be a T-subspace lattice on a Banach space X, AlgL be the associated reflexive algebra and A be a subalgebra of AlgL containing all finite rank operators in AlgL. If either dimK = infinity or dimK(-)(perpendicular to) = infinity for every K is an element of L with K not equal (0) and K- not equal 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) subset of X -- > X with its domain Dom(T) invariant under every element of A, such that D(A)x = (TA - AT)x for all A is an element of A and X is an element of Dom(T). This result can apply to those reflexive algebras with atomic Boolean subspace lattices and pentagon subspace lattices, respectively.
Journal Title
Houston Journal of Mathematics
Volume
32
Issue/Number
2
Publication Date
1-1-2006
Document Type
Article
Language
English
First Page
521
Last Page
530
WOS Identifier
ISSN
0362-1588
Recommended Citation
"Additive derivations of certain reflexive algebras" (2006). Faculty Bibliography 2000s. 6346.
https://stars.library.ucf.edu/facultybib2000/6346
Comments
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