On coincidence of Pettis and McShane integrability

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00443124" target="_blank" >RIV/67985840:_____/15:00443124 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10587-015-0161-x" target="_blank" >http://dx.doi.org/10.1007/s10587-015-0161-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10587-015-0161-x" target="_blank" >10.1007/s10587-015-0161-x</a>

Result language
angličtina
Original language name
On coincidence of Pettis and McShane integrability
Original language description
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 scalarlynull (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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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