We consider the transformation $\ev$ which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both $\ev$ and its dual $\ev^*$ are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. The answer is nontrivial for various choices of K and A already for A=K[x], the polynomial ring in one variable. Applications to the structure of algebras of cohomology operations are given.
|Translated title of the contribution||The discrete Gelfand transform and its dual|
|Pages (from-to)||184 - 186|
|Journal||Uspekhi Matematicheskikh Nauk (Russian Mathematical Journal)|
|Publication status||Published - Apr 2004|