Köthe coechelon spaces as locally convex algebras
Volume 199 / 2010
Studia Mathematica 199 (2010), 241-265
MSC: Primary 46J05; Secondary 46A04, 46A45, 46A13, 46J20.
DOI: 10.4064/sm199-3-3
Abstract
We study those Köthe coechelon sequence spaces $k_p(V)$, $1 \leq p \leq \infty$ or ${p=0}$, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix $V=(v_n)_n$ when an algebra $k_p(V)$ is unital, locally m-convex, a $\mathcal{Q}$-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.
