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CAMILLO TRAPANI

Representable linear functionals on partial ∗-algebras

  • Authors: Bagarello,F; Inoue, A; Trapani, C
  • Publication year: 2012
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: representations; positive linear functionals; partial *-algebras
  • OA Link: http://hdl.handle.net/10447/63417

Abstract

A GNS-like *-representation of a partial *-algebra A defined by certain representable linear functionals on A is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.