Admissibility of weights on non-normed *-algebras

Abstract

The notion of weights on (topological) *-algebras is defined and studied. The primary purpose is to define the notions of admissibility and approximate admissibility of weights, and to investigate when a weight is admissible or approximately admissible. The results obtained are applied to vector weights and tracial weight on unbounded operator algebras, as well as to weights on smooth subalgebras of a C^*-algebra.