Geodesic
Pseudotrees and equivalent norms in the continuous. Functions spaces
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2007), pp. 5-11 
S. P. Gul'ko; M. S. Kobylina. Pseudotrees and equivalent norms in the continuous. Functions spaces. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2007), pp. 5-11. http://geodesic.mathdoc.fr/item/VTGU_2007_1_a0/
@article{VTGU_2007_1_a0,
     author = {S. P. Gul'ko and M. S. Kobylina},
     title = {Pseudotrees and equivalent norms in the continuous. {Functions} spaces},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--11},
     year = {2007},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2007_1_a0/}
}
TY  - JOUR
AU  - S. P. Gul'ko
AU  - M. S. Kobylina
TI  - Pseudotrees and equivalent norms in the continuous. Functions spaces
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2007
SP  - 5
EP  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTGU_2007_1_a0/
LA  - ru
ID  - VTGU_2007_1_a0
ER  - 
%0 Journal Article
%A S. P. Gul'ko
%A M. S. Kobylina
%T Pseudotrees and equivalent norms in the continuous. Functions spaces
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2007
%P 5-11
%N 1
%U http://geodesic.mathdoc.fr/item/VTGU_2007_1_a0/
%G ru
%F VTGU_2007_1_a0

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

A class of the pseudotrees is considered. We construct locally compact extension of a pseudotree, which also has the structure of a pseudotree. We prove that the space $C_0(T)$ of all continuous functions on a locally compact pseudotree $T$ admits a locally uniform rotund (LUR) renorming if the related space $C_0(P)$ admits such norm for every subtree $P$ of $T$ and an initial segments of $T$ are separable.

[1] Kobylina M.S., “Lokalno ravnomerno vypuklaya norma na prostranstve vida $C(K)$, gde $K$ –lineino uporyadochennyi separabelnyi kompakt”, Vestnik TGU, 2006, no. 290, 64–65

[2] Burke M.R., “Borel measurability of separately continuous function”, Topology and Its Applications, 129 (2003), 29–65 | DOI | MR | Zbl

[3] Deville R., Godefroy G., Zizler V., Smoothness and renorming in Banach spaces, Pitman monographs, 64, Pitman, N.Y., 1993 | MR | Zbl

[4] Haydon R.G., “Trees in renorming theory”, Proc. London Math. Soc., 78 (1999), 541–584 | DOI | MR | Zbl

[5] Kurepa D., “Ensembles ordonnés et ramifies”, Publ. Math. Univ. Belgrad, 4 (1935), 1–138 | Zbl

[6] Molto A., Orihuela J., Troyanski S., Valdivia M., A non linear transfer technique for renorming, Pre-Publicationes del Departamento de Matematicas, Universidad de Murcia 20, 2003

[7] Zizler V., “Locally uniformly rotund renorming and decomposition of Banach spaces”, Bull. Austr. Math. Soc., 29 (1984), 259–265 | DOI | MR | Zbl