Geodesic
An Infinite-Dimensional Version of the Borsuk--Ulam Theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 1-5

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

We study the solvability of the equation $a(x)=f(x)$ on a sphere in a Banach space, where $a$ is a closed surjective linear operator and $f$ is an odd $a$-compact map. We also estimate the topological dimension of the solution set and give applications of the corresponding theorem to some problems in differential equations and other fields of mathematics.
Keywords: closed surjective operator, compact map, operator equation. 
@article{FAA_2004_38_4_a0,
     author = {B. D. Gel'man},
     title = {An {Infinite-Dimensional} {Version} of the {Borsuk--Ulam} {Theorem}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--5},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a0/}
}
TY  - JOUR
AU  - B. D. Gel'man
TI  - An Infinite-Dimensional Version of the Borsuk--Ulam Theorem
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2004
SP  - 1
EP  - 5
VL  - 38
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a0/
LA  - ru
ID  - FAA_2004_38_4_a0
ER  - 
%0 Journal Article
%A B. D. Gel'man
%T An Infinite-Dimensional Version of the Borsuk--Ulam Theorem
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2004
%P 1-5
%V 38
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a0/
%G ru
%F FAA_2004_38_4_a0
B. D. Gel'man. An Infinite-Dimensional Version of the Borsuk--Ulam Theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 1-5. http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a0/