Geodesic
On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 1, pp. 79-83.

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

The present paper is devoted to the study of the solvability and dimension of the solution set of the equation $A (x) = f (x)$ on the sphere of a Hilbert space, in the case when A is a closed surjective operator and f a Lipschitz odd mapping. This theorem is a certain "analogue" of the infinite-dimensional version of the Borsuk-Ulam theorem.
Keywords: Borsuk–Ulam theorem, surjective operator, contractive mappings, Lipschitz constant, topological dimension. 
@article{FAA_2019_53_1_a6,
     author = {B. D. Gel'man},
     title = {On the {Borsuk--Ulam} theorem for {Lipschitz} mappings in an infinite-dimensional space},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {79--83},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/}
}
TY  - JOUR
AU  - B. D. Gel'man
TI  - On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2019
SP  - 79
EP  - 83
VL  - 53
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/
LA  - ru
ID  - FAA_2019_53_1_a6
ER  - 
%0 Journal Article
%A B. D. Gel'man
%T On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2019
%P 79-83
%V 53
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/
%G ru
%F FAA_2019_53_1_a6
B. D. Gel'man. On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 1, pp. 79-83. http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/

[1] J. Dugundji, A. Granas, Fixed Point Theory, PWN, Warszawa, 1982 | MR | Zbl

[2] H. Steinlein, Topological Methods in Nonlinear Analysis, Presses Univ. Montreal, Montreal, 1985, 166–235 | MR

[3] B. D. Gelman, Matem. sb., 193:1 (2002), 83–92 | DOI | MR | Zbl

[4] P. S. Aleksandrov, B. A. Pasynkov, Vvedenie v teoriyu razmernosti, Nauka, M., 1973 | MR

[5] V. Gurevich, G. Volmen, Teoriya razmernosti, IL, M., 1948

[6] B. D. Gelman, Funkts. analiz i ego pril., 38:4 (2004), 1–5 | DOI | MR | Zbl

[7] B. D. Gelman, Matem. sb., 207:6 (2016), 79–92 | DOI | Zbl