User jochen wengenroth - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T14:40:45Z http://mathoverflow.net/feeds/user/21293 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/80021/entire-calculus-and-clmc-algebras/88116#88116 Answer by Jochen Wengenroth for Entire calculus and clmc algebras Jochen Wengenroth 2012-02-10T16:42:15Z 2012-02-10T16:42:15Z <p>At least for commutative and completely metrizable locally convex algebras there is a theorem of Mityagin, Rolewicz, and Zelasko (Studia Math. 21 (1962), 291-306) which says that the algebra has to be locally m-comvex if all entire functions operate on it (meaning that $f(a)=\sum\limits_{n=0}^\infty\frac{ f^{(n)}(0)}{n!} a^n$ converges for all entire functions $f$ and all elements of the algebra).</p>