The cofinal property of the reflexive indecomposable Banach spaces

Spiros A. Argyros; Theocharis Raikoftsalis

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Banach spaces without minimal subspaces – Examples

Valentin Ferenczi, Christian Rosendal (2012)

Annales de l’institut Fourier

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We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11],by classifying them according to which side of the dichotomies they fall.

On the structure of ultraproducts of real interpolation spaces.

J. A. López Molina, M. E. Puerta, M. J. Rivera (2001)

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(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

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We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space $ℓ^{1} (ℕ)$ , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for $c_{0} (ℕ)$ or $ℓ^{p} (ℕ)$ , $1 < p < \infty$ . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.