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.
Bagarello, F., Inoue, A., Trapani, C. (2012). Representable linear functionals on partial ∗-algebras. MEDITERRANEAN JOURNAL OF MATHEMATICS, 9(1), 153-163 [10.1007/s00009-011-0118-8].
Representable linear functionals on partial ∗-algebras
BAGARELLO, Fabio;TRAPANI, Camillo
2012-01-01
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.
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