The tensor algebra of power series spaces

• Autorzy: Dietmar Vogt
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H20: Structure, classification of topological algebras
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A63: Topological invariants ((DN), ( Ω ), etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 2
• Strony: 189-202

Daty

wydano

2009

Twórcy

autor

Dietmar Vogt

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

Identyfikatory

DOI

10.4064/sm193-2-5