On coincidence of Pettis and McShane integrability

0443124 - MÚ 2016 RIV CZ eng J - Journal Article
Fabian, Marián
On coincidence of Pettis and McShane integrability.
Czechoslovak Mathematical Journal. Roč. 65, č. 1 (2015), s. 83-106. ISSN 0011-4642. E-ISSN 1572-9141
R&D Projects: GA ČR(CZ) GAP201/12/0290
Institutional support: RVO:67985840
Keywords : Pettis integral * McShane integral * MC-filling family
Subject RIV: BA - General Mathematics
Impact factor: 0.284, year: 2015
http://link.springer.com/article/10.1007/s10587-015-0161-x

R. Deville and J. Rodriguez proved that, for every Hilbert generated space X, every Pettis integrable function f[0,1]X is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space X and a scalarly null (hence Pettis integrable) function from [0,1] into X, which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from [0,1] (mostly) into C(K) spaces. We focus in more detail on the behavior of several concrete Eberlein (Corson) compact spaces K, that are not uniform Eberlein, with respect to the integrability of some natural scalarly negligible functions from [0,1] into C(K) in McShane sense.
Permanent Link: http://hdl.handle.net/11104/0245880