In this paper, we show Hilbert C∗-module versions of Hölder– McCarthy inequality and its complementary inequality. As an application, we obtain Hölder type inequalities and its reverses on a Hilbert C∗-module.

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

Abstract In this paper we show that every conjugation C on the Hardy-Hilbert space H 2 is of type = T *