Bessaga's conjecture in unstable Köthe spaces and products

Nurlu, Zefer; Sarsour, Jasser

Studia Mathematica, Tome 104 (1993), p. 221-228 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $l i m_{n} (d_{n + 1} (U_{q}, U_{p})) / (d_{n} (U_{r}, U_{s})) = 0$ where $d_{n} (U, V)$ denotes the nth Kolmogorov diameter.

Publié le : 1993-01-01

Zbl 0812.46004

EUDML-ID : urn:eudml:doc:215971

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     author = {Zefer Nurlu and Jasser Sarsour},
     title = {Bessaga's conjecture in unstable K\"othe spaces and products},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {221-228},
     zbl = {0812.46004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p221bwm}
}

Nurlu, Zefer; Sarsour, Jasser. Bessaga's conjecture in unstable Köthe spaces and products. Studia Mathematica, Tome 104 (1993) pp. 221-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p221bwm/

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