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Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Xinxing Wu (2014)

Czechoslovak Mathematical Journal

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator B w n : λ p ( A ) λ p ( A ) defined on the Köthe sequence space λ p ( A ) exhibits distributional ϵ -chaos for any 0 < ϵ < diam λ p ( A ) and any n is obtained. Under this assumption, the principal measure of B w n is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional ϵ -chaos for any 0 < ϵ < diam λ p ( A ) .

Maximal equicontinuous factors and cohomology for tiling spaces

Marcy Barge, Johannes Kellendonk, Scott Schmieding (2012)

Fundamenta Mathematicae

We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.

Maximal scrambled sets for simple chaotic functions.

Víctor Jiménez López (1996)

Publicacions Matemàtiques

This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.

Means on scattered compacta

T. Banakh, R. Bonnet, W. Kubis (2014)

Topological Algebra and its Applications

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

Measurable functionals on function spaces

J. P. Reus Christensen, J. K. Pachl (1981)

Annales de l'institut Fourier

We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.

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