Isometries of non-self-adjoint operator algebras
The paper is devoted to the study of isometries of certain non selfadjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial Jordan triple product. A family \({\mathfrak N}\) of projections in B(H) is called a nest if it is totally ordered and contains 0 and I. \({\mathfrak N}\) is said to be complete if it is closed in the strong operator topology. The nest algebra alg \({\mathfrak N}\) associated with \({\mathfrak N}\) is defined as \[ alg {\mathfrak N}=\{T\in B(H):\;(I-P)TP=0\text{ for all } P\in {\mathfrak N}\}. \] The main result of the paper says that if \({\mathfrak N}\) and \({\mathfrak M}\) are complete nests of projection in B(H) then any linear isometry between alg \({\mathfrak N}\) and alg \({\mathfrak M}\) is of the form \(T\mapsto UTW\) or \(T\mapsto UJT^*JW\), where U, V are suitable unitary operators and J a fixed involution of H.
isometries of certain non selfadjoint operator algebras
structure of the complete holomorphic vector fields on their unit
scientific article; zbMATH DE number 4173684
scientific article