A Banach Algebraic Approach to the Borsuk-Ulam Theorem. (8th March 2012)

• Record Type: Journal Article
• Authors: Taghavi, Ali
• Other Names: Perez-Garcia David Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-03-08
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/729745
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.