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) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras with (Ω) as quotient algebras of and Fréchet m-algebras with (DN) and (Ω) as quotient algebras of with respect to a complemented ideal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-5,
author = {Dietmar Vogt},
title = {The tensor algebra of power series spaces},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {189-202},
zbl = {1200.46040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-5}
}
Dietmar Vogt. The tensor algebra of power series spaces. Studia Mathematica, Tome 192 (2009) pp. 189-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-2-5/