Maximal extensions of a linear functional
Authors : Fabio Burderi, Camillo Trapani, Salvatore Triolo
Pages : 198-209
Doi:10.33205/cma.1310238
View : 194 | Download : 229
Publication Date : 2023-12-15
Article Type : Research
Abstract :Extensions of a positive hermitian linear functional $\\omega$, defined on a dense *-subalgebra $\\mathfrak{A_{0}}$ of a topological *-algebra $\\mathfrak{A}[\\tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.Keywords : Positive linear functionals, Topological *-algebras, , Extension of linear functionals