Geodesic
Examples of Sets with Given Approximation Properties in $WCG$-Space
Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 643-647.

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

An example of a nontrivial convex bounded Chebyshev set is constructed in an arbitrary weakly compactly generated Banach space ($WCG$-space). An example of bounded approximately compact but not locally compact set is constructed in an arbitrary infinite-dimensional $WCG$-space.
Keywords: approximative compactness, weakly compactly generated Banach space, locally compact set, Chebyshev set. 
@article{MZM_2013_94_5_a0,
     author = {P. A. Borodin},
     title = {Examples of {Sets} with {Given} {Approximation} {Properties} in $WCG${-Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--647},
     publisher = {mathdoc},
     volume = {94},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a0/}
}
TY  - JOUR
AU  - P. A. Borodin
TI  - Examples of Sets with Given Approximation Properties in $WCG$-Space
JO  - Matematičeskie zametki
PY  - 2013
SP  - 643
EP  - 647
VL  - 94
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a0/
LA  - ru
ID  - MZM_2013_94_5_a0
ER  - 
%0 Journal Article
%A P. A. Borodin
%T Examples of Sets with Given Approximation Properties in $WCG$-Space
%J Matematičeskie zametki
%D 2013
%P 643-647
%V 94
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a0/
%G ru
%F MZM_2013_94_5_a0
P. A. Borodin. Examples of Sets with Given Approximation Properties in $WCG$-Space. Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 643-647. http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a0/

[1] N. V. Efimov, S. B. Stechkin, “Nekotorye svoistva chebyshevskikh mnozhestv”, Dokl. AN SSSR, 118:1 (1958), 17–19 | MR | Zbl

[2] N. V. Efimov, S. B. Stechkin, “Approksimativnaya kompaktnost i chebyshevskie mnozhestva”, Dokl. AN SSSR, 140:3 (1961), 522–524 | MR | Zbl

[3] L. P. Vlasov paper Approksimativnye svoistva mnozhestv v lineinykh normirovannykh prostranstvakh, UMN, 28:6 (1973), 3–66 | MR | Zbl

[4] P. A. Borodin, “Primer ogranichennogo approksimativno kompaktnogo mnozhestva, ne yavlyayuschegosya kompaktnym”, UMN, 49:4 (1994), 157–158 | MR | Zbl

[5] I. A. Pyatyshev, “Primer ogranichennogo approksimativno kompaktnogo mnozhestva, ne yavlyayuschegosya lokalno kompaktnym”, UMN, 62:5 (2007), 163–164 | DOI | MR | Zbl

[6] P. A. Borodin, “O vypuklykh approksimativno kompaktnykh mnozhestvakh i prostranstvakh Efimova–Stechkina”, Vestn. Mosk. un-ta. Ser. 1 Matem., mekh., 1999, no. 4, 19–21 | MR | Zbl

[7] W. J. Davis, T. Figiel, W. B. Johnson, A. Pełczyński, “Factoring weakly compact operators”, J. Funct. Anal., 17:3 (1974), 311–327 | DOI | MR | Zbl

[8] Dzh. Distel, Geometriya banakhovykh prostranstv. Izbrannye glavy, Vischa shkola, Kiev, 1980 | MR | Zbl

[9] S. Troyanski, “On locally uniformly convex and differentiable norms in certain non-separable Banach spaces”, Studia Math., 37:2 (1971), 173–180 | MR | Zbl

[10] N. Danford, Dzh. Shvarts, Lineinye operatory. T. 1. Obschaya teoriya, IL, M., 1962 | MR | Zbl

[11] I. A. Pyatyshev, “Primer vypuklogo approksimativno kompaktnogo tela v prostranstve $c_0$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2005, no. 3, 57–59 | MR | Zbl