Annals of Functional Analysis

Integral functionals on $C^*$-algebra of vector-valued regulated functions

R‎. ‎Arbach and L‎. ‎A‎. ‎O‎. ‎Fernandes

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‎In this paper we deal with the notion of regulated functions with‎ ‎values in a $C^*$-algebra $ \mathcal A $ and present examples using‎ ‎a special bi-dimensional $C^*$-algebra of triangular matrices‎. ‎We‎ ‎consider the Dushnik integral for these functions and shows that a‎ ‎convenient choice of the integrator function produces an integral‎ ‎homomorphism on the $C^*$-algebra of all regulated functions $‎ ‎G([a,b],\mathcal A) $‎. ‎Finally we construct a family of linear‎ ‎integral functionals on this $C^*$-algebra‎.

Article information

Ann. Funct. Anal., Volume 3, Number 2 (2012), 21-31.

First available in Project Euclid: 12 May 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46K05: General theory of topological algebras with involution
Secondary: 45N05‎ ‎46C05

$C^*$-Algebras ‎regulated Function ‎Dushnik Integral


‎Fernandes, L‎. ‎A‎. ‎O‎.; ‎Arbach, R‎. Integral functionals on $C^*$-algebra of vector-valued regulated functions. Ann. Funct. Anal. 3 (2012), no. 2, 21--31. doi:10.15352/afa/1399899930.

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