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Representable Linear Functionals on Partial *-Algebras |
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| Authors: | Fabio Bagarello Atsushi Inoue Camillo Trapani |
| Institution: | 1. Dipartimento di Metodi e Modelli Matematici, Fac. Ingegneria, Universit?? di Palermo, I-90128, Palermo, Italy 2. Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan 3. Dipartimento di Matematica e Informatica, Universit?? di Palermo, I-90123, Palermo, Italy |
| Abstract: | A GNS-like *-representation of a partial *-algebra \mathfrak A{{\mathfrak A}} defined by certain representable linear functionals on \mathfrak A{{\mathfrak 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. |
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