Admissibility of Weights on Non-normed $*$-Algebras

Abstract

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.

Unbounded $C$*-Seminorms and *-Representations of Partial *-Algebras

“…They have been extensively studied in the literature; see, e.g. [9][10][11][12][13]19]. One of the main points of the theory is that every *-representation of the completion (A, p) is bounded.…”