Integral functionals on c*-algebra of vector-valued regulated functions

Abstract

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 G([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra. © 2012, Duke University Press. All rights reserved.