Geodesic
Norm-attaining functionals on $C(Q,X)$
Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 45-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

Functionals (vector measures) defined on the space $C(Q,X)$ of continuous abstract functions (where $Q$ is a compact Hausdorff space and $X$ is a Banach space) and attaining their norm on the unit sphere are considered. A characterization of such functionals is given in terms of the Radon–Nikodym derivative of the vector measure with respect to the variation of the measure and in terms of analogs of the derivative. Applications to the characterization of finite-codimensional subspaces with the best approximation property are given. Similar results are obtained for the space $B(Q,\Sigma,X)$ of uniform limits of simple functions. 
@article{MZM_1997_61_1_a5,
     author = {L. P. Vlasov},
     title = {Norm-attaining functionals on $C(Q,X)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {45--56},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a5/}
}
TY  - JOUR
AU  - L. P. Vlasov
TI  - Norm-attaining functionals on $C(Q,X)$
JO  - Matematičeskie zametki
PY  - 1997
SP  - 45
EP  - 56
VL  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a5/
LA  - ru
ID  - MZM_1997_61_1_a5
ER  - 
%0 Journal Article
%A L. P. Vlasov
%T Norm-attaining functionals on $C(Q,X)$
%J Matematičeskie zametki
%D 1997
%P 45-56
%V 61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a5/
%G ru
%F MZM_1997_61_1_a5
L. P. Vlasov. Norm-attaining functionals on $C(Q,X)$. Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 45-56. http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a5/

[1] Distel Dzh., Geometriya banakhovykh prostranstv, Vischa shkola, Kiev, 1980

[2] Singer I., Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, Berlin, 1970

[3] Ustinov G. M., Shashkin Yu. A., “O funktsionalakh, dostigayuschikh normy”, Issledovaniya po funktsionalnomu analizu i ego prilozheniyam, Sb. nauch. tr. UrGU, Sverdlovsk, 1985, 103–109 | Zbl

[4] Ustinov G. M., “O podprostranstvakh suschestvovaniya v $C(Q,X)$”, Issledovaniya po funktsionalnomu analizu i topologii, Sb. nauch. tr. UrGU, Sverdlovsk, 1990, 127–130 | MR | Zbl

[5] Vlasov L. P., “Suschestvovanie elementov nailuchshego priblizheniya v $C(Q,X)$”, Matem. zametki, 58:2 (1995), 163–175 | MR | Zbl

[6] Zinger I., “Lineinye funktsionaly na prostranstve nepreryvnykh otobrazhenii bikompaktnogo khausdorfovogo prostranstva v prostranstvo Banakha”, Revue Roun. Math. Pur. Appl., 2 (1957), 301–315 | Zbl

[7] Burbaki N., Integrirovanie (Vektornoe integrirovanie. Mera Khaara. Svertka i predstavleniya), Nauka, M., 1970

[8] Danford N., Shvarts Dzh., Lineinye operatory (obschaya teoriya), IL, M., 1962

[9] Balaganskii V. S., Vlasov L. P., Approksimativno-geometricheskie svoistva mnozhestv v banakhovykh prostranstvakh, Preprint IMM UrO AN SSSR, Sverdlovsk, 1990

[10] Bessaga C., Pełczyński A., Selected topics in infinitedimensional topology, Monogr. Mat., 58, PWN, Warsawa, 1975 | MR | Zbl

[11] Engelking R., Obschaya topologiya, Mir, M., 1986

[12] Arkhangelskii A. V., Ponomarev V. I., Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974