Displaying similar documents to “Operators whose adjoints are quasi p-nuclear”

Bessaga's conjecture in unstable Köthe spaces and products

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 ( 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...

On multilinear generalizations of the concept of nuclear operators

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...