Search results for "Approximate identity"

Well-behaved *-Representations

2002

This chapter is devoted to the study of the so-called well-behaved *-representations of (partial) *-algebras. Actually one may define are two notions of well-behavedness and we will discuss the relation between them. These notions are introduced in order to avoid pathologies which may arise for general *-representations and to select “nice” representations, which may have a richer theory. In Section 8.1, we construct a class {π p } of *-representations, starting from an unbounded C*-seminorm p and we define nice *-representations in {π p }, called well-behaved. We also characterize their existence. In Section 8.2, we introduce the well-behaved *-representations associated with a compatible …