We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-2-4,
author = {Pawe\l\ Doma\'nski and Michael Langenbruch},
title = {Algebra of multipliers on the space of real analytic functions of one variable},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {155-171},
zbl = {1268.46021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-2-4}
}
Paweł Domański; Michael Langenbruch. Algebra of multipliers on the space of real analytic functions of one variable. Studia Mathematica, Tome 209 (2012) pp. 155-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-2-4/