JournalsprimsVol. 26 , No. 2DOI 10.2977/prims/1195171084

Partial *-Algebras of Closable Operators. I. The Basic Theory and the Abelian Case

  • Jean-Pierre Antoine

    Université Catholique de Louvain, Louvain-La-Neuve, Belgium
  • Atsushi Inoue

    Hiroshima University, Japan
  • Camillo Trapani

    Università degli Studi di Palermo, Italy
Partial *-Algebras of Closable Operators. I. The Basic Theory and the Abelian Case cover

Abstract

This paper, the first of two, is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial Op*-algebras). After setting up the basic definitions, we describe canonical extensions of partial Op*-algebras by closure and introduce a new bounded commutant, called quasi-weak. We initiate a theory of abelian partial *-algebras. As an application, we analyze thoroughly the partial Op*-algebras generated by a single closed symmetric operator.