Maximal extensions of a linear functional

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Constructive Mathematical Analysis
Volume:6 Issue:4
Maximal extensions of a linear functional

Maximal extensions of a linear functional

Authors : Fabio Burderi, Camillo Trapani, Salvatore Triolo

Pages : 198-209

Doi:10.33205/cma.1310238

View : 202 | Download : 236

Publication Date : 2023-12-15

Article Type : Research Paper

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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