Operator valued integral multiplier functions

Abstract

In recent years, several papers were devoted to the study of (p, q)-summing sequences of operators and their applications in the theory of Banach spaces. In the present paper we initiate a similar study of “integral multiplier functions”, thereby introducing these spaces of operator valued multiplier functions as normed spaces, establishing the basic results needed in such a theory and considering applications to the characterization of classical (operator valued) function spaces and spaces of operators on (or into) classical function spaces. We prove some significant “measurability results” for operator valued functions and apply these to establish several “function space versions” of results in the (p, q)-summing sequence setting.

Keywords: Bochner integral, weakly* p-integrable function, weak p-integrable function, integral multiplier function, (p, q)-integral function, (p, q)*-integrable function

Quaestiones Mathematicae 29(2006), 407–426