A remark on p-absolutely summing operators in -spaces
S. Kwapień (1970)
Studia Mathematica
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S. Kwapień (1970)
Studia Mathematica
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Bernd Carl (1983)
Studia Mathematica
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H. Millington (1974)
Mathematische Annalen
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A.K. Katsaras (1995)
Annales mathématiques Blaise Pascal
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Zefer Nurlu, Jasser Sarsour (1993)
Studia Mathematica
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Let F be a complemented subspace of a nuclear Fréchet space E. If E and F both have (absolute) bases resp. , then Bessaga conjectured (see [2] and for a more general form, also [8]) that there exists an isomorphism of F into E mapping to where is a scalar sequence, π is a permutation of ℕ and is a subsequence of ℕ. We prove that the conjecture holds if E is unstable, i.e. for some base of decreasing zero-neighborhoods consisting of absolutely convex sets one has ∃s ∀p ∃q...
Dahmane Achour, Ahlem Alouani (2010)
Colloquium Mathematicae
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This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear...
Hans Jarchow, Kamil John (1994)
Czechoslovak Mathematical Journal
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M. Ramanujan, T. Terzioglu (1975)
Studia Mathematica
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