A Constructive Proof of the Generalized Gelfand Isomorphism
 V. M. Buchstaber,
 E. G. Rees
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Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius \(\user1{n}\) homomorphism. For \(\user1{n} = 1\) , this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space, \(Sym^\user1{n} (X)\) the \(\user1{n}\) th symmetric power of X, and \(\mathbb{C}(M)\) the algebra of continuous complexvalued functions on X with the supnorm; then the evaluation map \({\mathcal{E}}:Sym^\user1{n} (X) \to Hom(\mathbb{C}(X),\mathbb{C})\) defined by the formula \([\user1{x}_1 , \ldots ,\user1{x}_\user1{n} ] \to (\user1{g} \to \sum {\user1{g}(} \user1{x}_\user1{k} ))\) identifies the space \(Sym^\user1{n} (X)\) with the space of all Frobenius \(\user1{n}\) homomorphisms of the algebra \((\mathbb{C}(X)\) into \(\mathbb{C}\) with the weak topology.
 V. M. Buchstaber and E. G. Rees, The Gelfand Map and Symmetric Products, Preprint, 2001; eprint uk.arXiv.org: math.CO/0109122.
 Title
 A Constructive Proof of the Generalized Gelfand Isomorphism
 Journal

Functional Analysis and Its Applications
Volume 35, Issue 4 , pp 257260
 Cover Date
 20011001
 DOI
 10.1023/A:1013170322564
 Print ISSN
 00162663
 Online ISSN
 15738485
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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 Authors

 V. M. Buchstaber ^{(1)}
 E. G. Rees ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Mechanics, Moscow State University, Russia
 2. Department of Mathematics and Statistics, Edinburgh University, UK