EXTENSIONS OF POSITIVE LINEAR FUNCTIONALS ON A TOPOLOGICAL *-ALGEBRA

被引：10

作者：

Bongiorno, Benedetto ^{[1
]}

Trapani, Camillo ^{[1
]}

Triolo, Salvatore ^{[1
]}

机构：

[1] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo, Italy

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2010年 / 40卷 / 06期

关键词：

Positive linear functionals; topological *-algebras;

D O I：

10.1216/RMJ-2010-40-6-1745

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The family of all extensions of a nonclosable hermitian positive linear functional defined on a dense *-subalgebra U(0) of a topological *-algebra U[tau] is studied with the aim of finding extensions that behave regularly. Under suitable assumptions, special classes of extensions (positive, positively regular, absolutely convergent) are constructed. The obtained results are applied to the commutative integration theory to recover from the abstract setup the well-known extensions of Lebesgue integral and, in noncommutative integration theory, for introducing a generalized non absolutely convergent integral of operators measurable with respect to a given trace sigma.

引用

页码：1745 / 1777

页数：33

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