# Extensions of positive linear functionals on a *-algebra

Risultato della ricerca: Article

10 Citazioni (Scopus)

### Abstract

The family of all extensions of a nonclosable hermitian positive linear functional defined on a dense *-subalgebra $\Ao$ of a topological *-algebra $\A[\tau]$is studied with the aim of finding extensions that behave regularly. Under suitable assumptions, special classesof extensions (positive, positively regular, absolutely convergent) are constructed. The obtained results areapplied to the commutative integration theory to recover from the abstract setup the well-known extensions ofLebesgue integral and, in noncommutative integration theory, for introducing a generalized non absolutelyconvergent integral of operators measurable w. r. to a given trace $\sigma$.
Lingua originale English 1745-1777 33 Default journal 40 Published - 2010

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Linear Functionals
Algebra
Topological Algebra
Linear Functional
Subalgebra
Trace
Operator

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

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In: Default journal, Vol. 40, 2010, pag. 1745-1777.

Risultato della ricerca: Article

title = "Extensions of positive linear functionals on a *-algebra",
abstract = "The family of all extensions of a nonclosable hermitian positive linear functional defined on a dense *-subalgebra $\Ao$ of a topological *-algebra $\A[\tau]$is studied with the aim of finding extensions that behave regularly. Under suitable assumptions, special classesof extensions (positive, positively regular, absolutely convergent) are constructed. The obtained results areapplied to the commutative integration theory to recover from the abstract setup the well-known extensions ofLebesgue integral and, in noncommutative integration theory, for introducing a generalized non absolutelyconvergent integral of operators measurable w. r. to a given trace $\sigma$.",
author = "Salvatore Triolo and Camillo Trapani and Benedetto Bongiorno",
year = "2010",
language = "English",
volume = "40",
pages = "1745--1777",
journal = "Default journal",

}

TY - JOUR

T1 - Extensions of positive linear functionals on a *-algebra

AU - Triolo, Salvatore

AU - Trapani, Camillo

AU - Bongiorno, Benedetto

PY - 2010

Y1 - 2010

N2 - The family of all extensions of a nonclosable hermitian positive linear functional defined on a dense *-subalgebra $\Ao$ of a topological *-algebra $\A[\tau]$is studied with the aim of finding extensions that behave regularly. Under suitable assumptions, special classesof extensions (positive, positively regular, absolutely convergent) are constructed. The obtained results areapplied to the commutative integration theory to recover from the abstract setup the well-known extensions ofLebesgue integral and, in noncommutative integration theory, for introducing a generalized non absolutelyconvergent integral of operators measurable w. r. to a given trace $\sigma$.

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

UR - http://hdl.handle.net/10447/40142

M3 - Article

VL - 40

SP - 1745

EP - 1777

JO - Default journal

JF - Default journal

ER -