Abstract and Applied Analysis

A Banach Algebraic Approach to the Borsuk-Ulam Theorem

Ali Taghavi

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Using methods from the theory of commutative graded Banach algebras, we obtain a generalization of the two-dimensional Borsuk-Ulam theorem as follows. Let ϕ : S 2 S 2 be a homeomorphism of order n , and let λ 1 be an n th root of the unity, then, for every complex valued continuous function f on S 2 , the function i = 0 n 1 λ i f ( ϕ i ( x ) ) must vanish at some point of S 2 . We also discuss some noncommutative versions of the Borsuk-Ulam theorem.

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Abstr. Appl. Anal., Volume 2012 (2012), Article ID 729745, 11 pages.

First available in Project Euclid: 14 December 2012

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Taghavi, Ali. A Banach Algebraic Approach to the Borsuk-Ulam Theorem. Abstr. Appl. Anal. 2012 (2012), Article ID 729745, 11 pages. doi:10.1155/2012/729745. https://projecteuclid.org/euclid.aaa/1355495655

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