Maximal extensions of a linear functional

Year 2023, , 198 - 209, 15.12.2023

Fabio Burderi , Camillo Trapanı , Salvatore Triolo

https://doi.org/10.33205/cma.1310238

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

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