Köthe coechelon spaces as locally convex algebras

José Bonet, and Paweł Domański. "Köthe coechelon spaces as locally convex algebras." Studia Mathematica 199.3 (2010): 241-265. <http://eudml.org/doc/285887>.

@article{JoséBonet2010,
abstract = {We study those Köthe coechelon sequence spaces $k_\{p\}(V)$, 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 $k_\{p\}(V)$ 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.},
author = {José Bonet, Paweł Domański},
journal = {Studia Mathematica},
keywords = {topological algebras; Riesz algebras; LB-spaces; coechelon spaces; Q-algebras; maximal ideals; regular ideals; characters; automatic continuity},
language = {eng},
number = {3},
pages = {241-265},
title = {Köthe coechelon spaces as locally convex algebras},
url = {http://eudml.org/doc/285887},
volume = {199},
year = {2010},
}

TY - JOUR
AU - José Bonet
AU - Paweł Domański
TI - Köthe coechelon spaces as locally convex algebras
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 3
SP - 241
EP - 265
AB - We study those Köthe coechelon sequence spaces $k_{p}(V)$, 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 $k_{p}(V)$ 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.
LA - eng
KW - topological algebras; Riesz algebras; LB-spaces; coechelon spaces; Q-algebras; maximal ideals; regular ideals; characters; automatic continuity
UR - http://eudml.org/doc/285887
ER -