Bessaga's conjecture in unstable Köthe spaces and products

• Autorzy: Zefer Nurlu , Jasser Sarsour
• Języki publikacji: EN

Abstrakty

EN

Let F be a complemented subspace of a nuclear Fréchet space E. If E and F both have (absolute) bases $(e_n)$ resp. $(f_n)$, then Bessaga conjectured (see [2] and for a more general form, also [8]) that there exists an isomorphism of F into E mapping $f_n$ to $t_n e_{π(k_n)}$ where $(t_n)$ is a scalar sequence, π is a permutation of ℕ and $(k_n)$ is a subsequence of ℕ. We prove that the conjecture holds if E is unstable, i.e. for some base of decreasing zero-neighborhoods $(U_n)$ consisting of absolutely convex sets one has ∃s ∀p ∃q ∀r $lim_n (d_{n+1}(U_q, U_p))/(d_n(U_r, U_s)) = 0$ where $d_n(U,V)$ denotes the nth Kolmogorov diameter.

Kategorie tematyczne

• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 3
• Strony: 221-228

Daty

wydano

1993

otrzymano

1991-12-17

poprawiono

1992-10-06

Twórcy

autor

Zefer Nurlu

• Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

autor

Jasser Sarsour

• Department of Mathematics, The Islamic University of Gaza, P.O. Box 108, Gaza, Gaza Strip

Bibliografia

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