Monotone operator functions on C*-algebra

الأصل · EN

The article is devoted to investigation of classes of functions monotone as functions on general C*-algebras that are not necessarily the C*-algebras of all bounded linear operators on a Hilbert space as it is in classical case of matrix and operator monotone functions. We show that for general C*-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of C*-algebras that have this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C*-algebras. We use this characterization to generalize one function based monotonicity conditions for commutativity of a C*-algebra, to one function based monotonicity conditions for subhomogeneity. As a C*-algebraic counterpart of standard matrix and operator monotone scaling, we investigate, by means of projective C*-algebras and relation lifting, the existence of C*-subalgebras of a given monotonicity class.