Affordable Access

Characterization of subspaces and quotients of nuclear $L_f (\alpha ,\infty)$-spaces

Publication Date
  • Law
  • Mathematics


Characterization of subspaces and quotients of nuclear Lf (,)-spaces COMPOSITIO MATHEMATICA HEIKKIAPIOLA Characterization of subspaces and quotients of nuclear L f (α,∞)-spaces Compositio Mathematica, tome 50, no 1 (1983), p. 65-81. <> © Foundation Compositio Mathematica, 1983, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: // implique l’accord avec les conditions gé- nérales d’utilisation ( Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 65 CHARACTERIZATION OF SUBSPACES AND QUOTIENTS OF NUCLEAR Lf (03B1, ~)-SPACES Heikki Apiola Compositio Mathematica 50 (1983) 65-81 @ 1983 Martinus Nijhoff Publishers, The Hague. Printed in the Netherlands Introduction In a series of important papers ([15-20]) D. Vogt and M.J. Wagner study the structure of subspaces and quotients of some classes of nuclear Kôthe spaces. They are able to give a complete basis free characterization in the case of stable power series spaces thus completing and generalizing to the basis free setting the study carried out by Alpseymen, Dubinsky, Robin- son and Wagner in [2], [4], [5]-[9], [21] and [22]. The method of Vogt and Wagner can be briefly described as a combination of the following steps: (1) Proving that under suitable topological conditions concerning the Fréchet spaces E and F, a short exact sequence of the form 0 - E - G - F - 0 splits. (2) Constructing exact sequences of power series spaces of the form 0 ~ ^r(03B1) ~ ^r(03B1) ~ 0. (3) Using a suitable generalization of the Komura embed- ding theorem. The purpose of the present paper is to study to which extent this method can

There are no comments yet on this publication. Be the first to share your thoughts.