#### 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.

http://stars.library.ucf.edu/facultybib2000/6346

## Comments

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