Isomorphism’s of Tensor Algebras Arising from Weighted Partial Systems

Classifying Non-Self-Adjoint Adjoint Tensor Operator Algebras

Abstract

Theo perator algebras associated to dynamical/topological/analytic objects, and their classification via these objects, have been the subject of study by many authors for almost 50 years, beginning with the work of Arveson [4] and Arveson and Josephson [13]. The main theme of this line of research, as is the main theme of this Paper, is to identify the extent to which the dynamical objects classify their associated non-self operator algebras. We shall mainly focus on classification of non-self-adjoint adjoint tensor operator algebras arising from a single C*-correspondence over a commutative C*-algebra, although a profusion of results have been obtained in other contexts to mention only some.