Geodesic
On coincidence of Pettis and McShane integrability
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 83-106

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

R. Deville and J. Rodríguez proved that, for every Hilbert generated space $X$, every Pettis integrable function $f\colon [0,1]\rightarrow X$ 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.
DOI : 10.1007/s10587-015-0161-x
Classification : 46B26, 46G10
Keywords: Pettis integral; McShane integral; MC-filling family; uniform Eberlein compact space; scalarly negligible function; Lebesgue injection; Hilbert generated space; strong Markuševič basis; adequate inflation 
@article{10_1007_s10587_015_0161_x,
     author = {Fabian, Mari\'an},
     title = {On coincidence of {Pettis} and {McShane} integrability},
     journal = {Czechoslovak Mathematical Journal},
     pages = {83--106},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {2015},
     doi = {10.1007/s10587-015-0161-x},
     mrnumber = {3336026},
     zbl = {06433722},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0161-x/}
}
TY  - JOUR
AU  - Fabian, Marián
TI  - On coincidence of Pettis and McShane integrability
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 83
EP  - 106
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0161-x/
DO  - 10.1007/s10587-015-0161-x
LA  - en
ID  - 10_1007_s10587_015_0161_x
ER  - 
%0 Journal Article
%A Fabian, Marián
%T On coincidence of Pettis and McShane integrability
%J Czechoslovak Mathematical Journal
%D 2015
%P 83-106
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0161-x/
%R 10.1007/s10587-015-0161-x
%G en
%F 10_1007_s10587_015_0161_x
Fabian, Marián. On coincidence of Pettis and McShane integrability. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 83-106. doi: 10.1007/s10587-015-0161-x

Cité par Sources :