INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS - Fernandes, L. A. O. [UNESP]; Arbach, R. [UNESP] (Tusi Mathematical Research Group, 2012)
In this paper we deal with the notion of regulated functions with values in a C*-algebra 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 ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.
Keywords: C*-Algebras; regulated Function; Dushnik Integral