Full paper in PDF:
$%A. Defant, P. Domański, and M. Mastyło, Extension and splitting theorems for Fréchet spaces of type 2, Rev. Mat. Complut. 12 (1999), no. 2, 325–337.%$

Extension and Splitting Theorems for Fréchet Spaces of Type 2
Andreas DEFANT, Paweł DOMAŃSKI,
and Mieczysław MASTYŁO
FE Mathematik
Carl von Ossietzky Universität
Amerländer Heerstraße 114-118
D-26111 Oldenburg — Germany
Institute of Mathematics (Poznań branch)
Polish Academy of Sciences
ul. Matejki 48/49
60-769 Poznań — Poland
Faculty of Mathematics and Computer Science
A. Mickiewicz University
ul. Matejki 48/49
60-769 Poznaui — Poland

Received: December 2, 1998
Revised: April 7, 1999

ABSTRACT

We prove the following common generalization of Maurey’s extension theorem and Vogt’s (DN)-(Ω  ) splitting theorem for Fréchet spaces: if T  is an operator from a subspace E  of a Fréchet space G  of type 2 to a Fréchet space F  of dual type 2, then T  extends to a map from G  into F′′ whenever G∕E  satisfies (DN) and F satisfies (Ω  ).

2000 Mathematics Subject Classification: primary 46A04, 46A22; secondary 46B70.