×

On Pelczynski’s problem. (English) Zbl 0804.46005

Advances in the theory of Fréchet spaces, Proc. NATO Adv. Res. Workshop, Istanbul/Turkey 1988, NATO ASI Ser., Ser. C 287, 297-304 (1989).
[For the entire collection see Zbl 0699.00024).]
In [Stud. Math. 38, 476 (1970)] A. Pelczynski asked, whether complemented subspaces of a nuclear Fréchet space with basis have a basis. This problem is equivalent to the question, whether complemented subspaces of nuclear Köthe spaces are again Köthe spaces.
Although this problem is still open, there are positive solutions in many special cases. The present article focusses on the methods of the proof of these results and their relations to D. Vogt’s splitting and structure theory [see Proc. of the same conf. e.g. pp. 11-27 (1989; Zbl 0711.46006)].

MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A35 Summability and bases in topological vector spaces
46A45 Sequence spaces (including Köthe sequence spaces)
PDFBibTeX XMLCite