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Système de Haar

B. Maurey (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Tauberian operators on L 1 ( μ ) spaces

Manuel González, Antonio Martínez-Abejón (1997)

Studia Mathematica

We characterize tauberian operators T : L 1 ( μ ) Y in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in L 1 [ 0 , 1 ] . As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator T : L 1 ( μ ) Y is also tauberian, and the induced operator T ̃ : L 1 ( μ ) * * / L 1 ( μ ) Y * * / Y is an isomorphism into. Also, we show that L 1 ( μ ) embeds...

Tensor product in symmetric function spaces.

S. V. Astashkin (1997)

Collectanea Mathematica

A concept of the multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows us to obtain some concrete results. In particular, the well-know theorem of R. O'Neil about boundedness of tensor product in the Lorentz spaces Lpq is discussed.

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