Additive derivations of certain reflexive algebras
Abbreviated Journal Title
Houst. J. Math.
additive derivations; quasi-spatiality; reflexive algebras; J-subspace; lattices; PENTAGON SUBSPACE LATTICES; STANDARD OPERATOR-ALGEBRAS; NEST-ALGEBRAS; ISOMORPHISMS; Mathematics
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.
Houston Journal of Mathematics
"Additive derivations of certain reflexive algebras" (2006). Faculty Bibliography 2000s. 6346.