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

TL;DR

This paper extends Gel'fand integration theory for operator-valued functions to Banach spaces, establishing conditions for $(q,p)$-summing integrals and addressing open questions with applications to positive operator functions.

Contribution

It introduces new conditions for Gel'fand integrals to be $(q,p)$-summing in Banach spaces and applies these results to positive operator-valued functions.

Findings

Provided sufficient conditions for $(q,p)$-summing Gel'fand integrals.

Answered an open question from previous literature.

Applied results to positive operator-valued functions.

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 \cite{M24} 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.