Gel’fand Integration of B(E,F∗)-Valued Functions With Emphasis on (q, p)-Summing Operators

Abstract

We generalize results concerning Gel’fand integration of functions taking values in the space of operators on Hilbert spaces to certain Banach spaces. Building on ideas from [10] we provide sufficient conditions for the Gel’fand integral to be (q,p)-summing and we use the developed techniques to answer a question posed in the mentioned article. Applications to positive operator-valued functions between certain function spaces are also given.