Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals |
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Authors: | Giorgia Bellomonte Camillo Trapani Salvatore Triolo |
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Affiliation: | (1) Departments of Bioengineering and Developmental Biology, University of Pittsburgh, 3501 Fifth Avenue, 5059-BST3, Pittsburgh, PA 15213, USA |
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Abstract: | The existence of extensions of a positive linear functional ω defined on a dense *-subalgebra mathfrakA0{mathfrak{A}_0} of a topological *-algebra mathfrakA{mathfrak{A}}, satisfying certain regularity conditions, is examined. The main interest is focused on the case where ω is nonclosable and sufficient conditions for the existence of an absolutely convergent extension of ω are given. |
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