6533b82afe1ef96bd128b5d4

RESEARCH PRODUCT

Well-behaved *-Representations

Camillo TrapaniAtsushi InoueJean-pierre Antoine

subject

Section (fiber bundle)Class (set theory)symbols.namesakePure mathematicsHilbert spacesymbolsOrder (ring theory)Linear spanApproximate identityAction (physics)Maximal elementMathematics

description

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 pair {A, X}, consisting of a *-algebra A and a normed *-algebra X with a left action of A on X. In Section 8.3, finally, we investigate the relation between the two types of well-behaved *-representations of *-algebras.

yearjournalcountryeditionlanguage
2002-01-01
https://doi.org/10.1007/978-94-017-0065-8_8