Representable linear functionals on partial *-algebras
Mathematical Physics
2012-07-10 v1 math.MP
Operator Algebras
Abstract
A GNS - like *-representation of a \pa\ defined by certain representable linear functionals on 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.
Cite
@article{arxiv.1207.2019,
title = {Representable linear functionals on partial *-algebras},
author = {Fabio Bagarello and Atsushi Inoue and Camillo Trapani},
journal= {arXiv preprint arXiv:1207.2019},
year = {2012}
}