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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 4, Pages 1–5
DOI: https://doi.org/10.4213/faa121 (Mi faa121) 		 
This article is cited in 12 scientific papers (total in 12 papers)

An Infinite-Dimensional Version of the Borsuk–Ulam Theorem

B. D. Gel'man

Voronezh State University
Full-text PDF (134 kB) Citations (12)
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DOI: https://doi.org/10.4213/faa121
Abstract: 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.
Received: 13.02.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 4, Pages 239–242
DOI: https://doi.org/10.1007/s10688-005-0001-0
Bibliographic databases:
Document Type: Article
UDC: 517.988.6
Language: Russian
Citation: B. D. Gel'man, “An Infinite-Dimensional Version of the Borsuk–Ulam Theorem”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 1–5; Funct. Anal. Appl., 38:4 (2004), 239–242
Citation in format AMSBIB
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\pages 1--5
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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