Geodesic
Köthe coechelon spaces as locally convex algebras
José Bonet1 ; Paweł Domański2
1 Instituto Universitario de Matemática Pura y Aplicada IUMPA Universidad Politécnica de Valencia E-46071 Valencia, Spain
2 Faculty of Mathematics and Computer Science A. Mickiewicz University Poznań Umultowska 87 61-614 Poznań, Poland
Studia Mathematica, Tome 199 (2010) no. 3, pp. 241-265 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm199-3-3
Keywords: study those coechelon sequence spaces leq leq infty which locally convex riesz algebras pointwise multiplication characterize terms matrix algebra unital locally m convex mathcal algebra has continuous quasi inverse entire functions act transcendental entire functions act proved multiplicative functionals continuous precise description regular degenerate maximal ideals given even arbitrary solid algebras sequences pointwise multiplication particular shown regular maximal ideals solid

José Bonet 1 ; Paweł Domański 2

1 Instituto Universitario de Matemática Pura y Aplicada IUMPA Universidad Politécnica de Valencia E-46071 Valencia, Spain
2 Faculty of Mathematics and Computer Science A. Mickiewicz University Poznań Umultowska 87 61-614 Poznań, Poland 
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José Bonet; Paweł   Domański. Köthe coechelon spaces as locally convex algebras. Studia Mathematica, Tome 199 (2010) no. 3, pp. 241-265. doi: 10.4064/sm199-3-3

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