A+ CATEGORY SCIENTIFIC UNIT

C*-seminorms on partial *-algebras: an overview

Volume 67 / 2005

Camillo Trapani Banach Center Publications 67 (2005), 369-384 MSC: Primary 46K05. 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.

Authors

  • Camillo TrapaniDipartimento di Matematica ed
    Applicazioni, Università di Palermo
    90123 Palermo, Italy
    e-mail

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