TY - JOUR
AU1 - Katavolos, A.
AU2 - Todorov, I. G.
AB - The set of normalizers between von Neumann (or, more generally, reflexive) algebras A and B (that is, the set of all operators T such that T A T* ⊆ B and T* B T ⊆ A) possesses ‘local linear structure’: it is a union of reflexive linear spaces. These spaces belong to the interesting class of normalizing linear spaces, namely, those linear spaces U of operators satisfying UU*U ⊆ U (also known as ternary rings of operators). Such a space is reflexive whenever it is ultraweakly closed, and then it is of the form U = T : TL = φ L T for all L ∈ L where L is a set of projections and φ a certain map defined on L. A normalizing space consists of normalizers between appropriate von Neumann algebras A and B. Necessary and sufficient conditions are found for a normalizing space to consist of normalizers between two reflexive algebras. Normalizing spaces which are bimodules over maximal abelian self‐adjoint algebras consist of operators ‘supported’ on sets of the form [f = g] where f and g are appropriate Borel functions. They also satisfy spectral synthesis in the sense of Arveson. 2000 Mathematical Subject Classification: 47L05 (primary), 47L35, 46L10 (secondary).
TI - Normalizers of Operator Algebras and Reflexivity
JF - Proceedings of the London Mathematical Society
DO - 10.1112/s0024611502013837
DA - 2003-03-01
UR - https://www.deepdyve.com/lp/wiley/normalizers-of-operator-algebras-and-reflexivity-Dcg0umvmrt
SP - 463
EP - 484
VL - 86
IS - 2
DP - DeepDyve
ER -