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On coincidence of Pettis and McShane integrability

SYSNO ASEP	0443124
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	On coincidence of Pettis and McShane integrability
Author(s)	Fabian, Marián (MU-W)_{RID, SAI, ORCID}
Source Title	Czechoslovak Mathematical Journal. - : Springer - ISSN 0011-4642 Roč. 65, č. 1 (2015), s. 83-106
Number of pages	24 s.
Language	eng - English
Country	CZ - Czech Republic
Keywords	Pettis integral ; McShane integral ; MC-filling family
Subject RIV	BA - General Mathematics
R&D Projects	GAP201/12/0290 GA ČR - Czech Science Foundation (CSF)
Institutional support	MU-W - RVO:67985840
UT WOS	000352820000004
EID SCOPUS	84938091191
DOI	10.1007/s10587-015-0161-x
Annotation	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.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2016

Number of the records: 1