The tensor algebra of power series spaces

Dietmar Vogt¹

¹ FB Mathematik und Naturwissenschaften Bergische Universität Wuppertal Gauß. 20 D-42097 Wuppertal, Germany

Studia Mathematica, Tome 193 (2009) no. 2, pp. 189-202

Résumé

The linear isomorphism type of the tensor algebra $T(E)$ of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always $s$, the situation for finite type power series spaces is more complicated. The linear isomorphism $T(s)\cong s$ can be used to define a multiplication on $s$ which makes it a Fréchet m-algebra $s_\bullet$. This may be used to give an algebra analogue to the structure theory of $s$, that is, characterize Fréchet m-algebras with ($\Omega$) as quotient algebras of $s_\bullet$ and Fréchet m-algebras with (DN) and ($\Omega$) as quotient algebras of $s_\bullet$ with respect to a complemented ideal.

Détail

DOI : 10.4064/sm193-2-5

Keywords: linear isomorphism type tensor algebra chet spaces particular power series spaces studied while nuclear power series spaces infinite type always situation finite type power series spaces complicated linear isomorphism cong define multiplication which makes chet m algebra bullet may algebra analogue structure theory characterize chet m algebras omega quotient algebras bullet chet m algebras omega quotient algebras bullet respect complemented ideal