The tensor algebra of power series spaces

Dietmar Vogt. "The tensor algebra of power series spaces." Studia Mathematica 193.2 (2009): 189-202. <http://eudml.org/doc/284879>.

@article{DietmarVogt2009,
abstract = {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 $s_\{•\}$. 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 $s_\{•\}$ and Fréchet m-algebras with (DN) and (Ω) as quotient algebras of $s_\{•\}$ with respect to a complemented ideal.},
author = {Dietmar Vogt},
journal = {Studia Mathematica},
keywords = {Fréchet -algebra; tensor algebra; power series space},
language = {eng},
number = {2},
pages = {189-202},
title = {The tensor algebra of power series spaces},
url = {http://eudml.org/doc/284879},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Dietmar Vogt
TI - The tensor algebra of power series spaces
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 2
SP - 189
EP - 202
AB - 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 $s_{•}$. 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 $s_{•}$ and Fréchet m-algebras with (DN) and (Ω) as quotient algebras of $s_{•}$ with respect to a complemented ideal.
LA - eng
KW - Fréchet -algebra; tensor algebra; power series space
UR - http://eudml.org/doc/284879
ER -