Author： Buchstaber V.M. Rees E.G.
Publisher： Springer Publishing Company
ISSN： 0016-2663
Source： Functional Analysis and Its Applications, Vol.35, Iss.4, 2001-10, pp. : 257-260
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Abstract
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius n-homomorphism. For n=1, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space, operatorname{Sym}^n(X) the nth symmetric power of X, and mathbb{C}(X) the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map mathcal{E}colonoperatorname{Sym}^n(X)tooperatorname{Hom}(mathbb{C}(X),mat hbb{C}) defined by the formula [x_1,dots,x_n]to(gtosum g(x_k)) identifies the space operatorname{Sym}^n(X) with the space of all Frobenius n-homomorphisms of the algebra mathbb{C}(X) into mathbb{C} with the weak topology.
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