INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES
BANACH CENTER
PUBLICATIONS
ISSN: 0137-6934(p) 1730-6299(e)
C*-seminorms on partial *-algebras: an overview
Camillo Trapani1 Banach Center Publ. 67 (2005), 369-384
doi:10.4064/bc67-0-30
Abstract:
The main facts about unbounded C*-seminorms on partial
*-algebras are reviewed and the link with the representation
theory is discussed. In particular, starting from the more
familiar case of *-algebras, we examine C*-seminorms that are
defined from suitable families of positive linear or sesquilinear
forms, mimicking the
construction of the Gelfand seminorm for Banach *-algebras. The
admissibility of these forms in terms of the (unbounded)
C*-seminorms they generate is characterized.
