The McShane integral in weakly compactly generated spaces
Antonio Avil\'es, Grzegorz Plebanek, Jos\'e Rodr\'iguez
TL;DR
This paper investigates the relationship between Pettis and McShane integrability in weakly compactly generated Banach spaces, providing a negative answer to a previously open question.
Contribution
It demonstrates that not all Pettis integrable functions in weakly compactly generated spaces are McShane integrable, resolving an open problem.
Findings
Counterexample showing Pettis integrability does not imply McShane integrability
Clarification of integrability distinctions in Banach spaces
Advancement in understanding integrability in functional analysis
Abstract
Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative.
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