Köthe coechelon spaces as locally convex algebras

• Autorzy: José Bonet , Paweł Domański
• Języki publikacji: EN

Abstrakty

EN

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 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.

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 3
• Strony: 241-265

Daty

wydano

2010

Twórcy

autor

José Bonet

• Instituto Universitario de Matemática, Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071 Valencia, Spain

autor

Paweł Domański

• Faculty of Mathematics and Computer Science, A. Mickiewicz University Poznań, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm199-3-3