A non-regular Toeplitz flow with preset pure point spectrum

T. Downarowicz; Y. Lacroix

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Displaying similar documents to “A non-regular Toeplitz flow with preset pure point spectrum”

Toeplitz flows with pure point spectrum

A. Iwanik (1996)

Studia Mathematica

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We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.

Some constructions of strictly ergodic non-regular Toeplitz flows

A. Iwanik, Y. Lacroix (1994)

Studia Mathematica

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We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.

The classification problem in Teoplitz $Z_{2}$ -extensions

Tadeusz Rojek (1989)

Compositio Mathematica

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Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers

Wojciech Bułatek, Jan Kwiatkowski (1992)

Studia Mathematica

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A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.

The topological centralizers of Toeplitz flows and their Z-extensions.

Wojciech Bulatek, Jan Kwiatkowski (1990)

Publicacions Matemàtiques

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The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z-extensions are described. Such Toeplitz flows are topologically coalescent. If {q, q, ...} is a set of all except at least one prime numbers and I, I, ... are positive integers then the direct sum ⊕ Z ⊕ Z can be the topological centralizer of a Toeplitz flow.

Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows

T. Downarowicz, Y. Lacroix (1998)

Studia Mathematica

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Let $(Z, T_{Z})$ be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of $(Z, T_{Z})$ is Borel isomorphic to an almost 1-1 extension of $(Z, T_{Z})$ . Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly...

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

On infinite bounded-Toeplitz extensions of Toeplitz matrices.

Il'in, S.N. (2004)

Zapiski Nauchnykh Seminarov POMI

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Spectral Radius and Spectrum of the Compression of a Slant Toeplitz Operator}

Taddesse Zegeye, S.C. Arora (2001)

Publications de l'Institut Mathématique

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A criterion for Toeplitz flows to be topologically isomorphic and applications

T. Downarowicz, J. Kwiatkowski, Y. Lacroix (1995)

Colloquium Mathematicae

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A dynamical system is said to be coalescent if its only endomorphisms are automorphisms. The question whether there exist coalescent ergodic dynamical systems with positive entropy has not been solved so far and it seems to be difficult. The analogous problem in topological dynamics has been solved by Walters ([W]). His example, however, is not minimal. In [B-K2], a class of strictly ergodic (hence minimal) Toeplitz flows is presented, which have positive entropy and trivial topological...

Deformation quantization and Borel's theorem in locally convex spaces

Miroslav Engliš, Jari Taskinen (2007)

Studia Mathematica

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It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth...