Generalized parallel sum of adjointable operators on Hilbert C*-modules

Abstract

ABSTRACT We introduce the notion of a tractable pair of operators as well as that of the generalized parallel sum in the setting of adjointable operators on Hilbert -modules. Some significant results about the parallel sum known for matrices and Hilbert space operators are extended to the case of the generalized parallel sum. In particular, a factorization theorem on the parallel sum is proved, and a common upper bound of two positive operators is constructed in the Hilbert -module case. The harmonic mean for positive operators on Hilbert -modules is also dealt with.