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ArticleOriginal scientific text

Title

Bessaga's conjecture in unstable Köthe spaces and products

Authors 1, 2

Affiliations

  1. Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
  2. Department of Mathematics, The Islamic University of Gaza, P.O. Box 108, Gaza, Gaza Strip

Abstract

Let F be a complemented subspace of a nuclear Fréchet space E. If E and F both have (absolute) bases (en) resp. (fn), then Bessaga conjectured (see [2] and for a more general form, also [8]) that there exists an isomorphism of F into E mapping fn to tneπ(kn) where (tn) is a scalar sequence, π is a permutation of ℕ and (kn) is a subsequence of ℕ. We prove that the conjecture holds if E is unstable, i.e. for some base of decreasing zero-neighborhoods (Un) consisting of absolutely convex sets one has ∃s ∀p ∃q ∀r limndn+1(Uq,Up)dn(Ur,Us)=0 where dn(U,V) denotes the nth Kolmogorov diameter.

Bibliography

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Studia Mathematica
1993/104/3
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Pages:
221-228
Main language of publication
English
Received
1991-12-17
Accepted
1992-10-06
Published
1993
Exact and natural sciences