We study those Köthe coechelon sequence spaces , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals is given even for arbitrary solid algebras of sequences with pointwise multiplication. In particular, it is shown that all regular maximal ideals are solid.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-3,
author = {Jos\'e Bonet and Pawe\l\ Doma\'nski},
title = {K\"othe coechelon spaces as locally convex algebras},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {241-265},
zbl = {1222.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-3}
}
José Bonet; Paweł Domański. Köthe coechelon spaces as locally convex algebras. Studia Mathematica, Tome 196 (2010) pp. 241-265. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-3/