<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:math>-crossed products and shift spaces

Carlsen, Toke Meier; Silvestrov, Sergei

doi:10.1016/j.exmath.2007.02.004

Cited by 20 publications

(2 citation statements)

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“…, n}. Exel [11] and Matsumoto [15] constructed C * -algebras associated to Λ. Carlsen and Silvestrov [4] unified the two constructions that led them to a C * -algebra O Λ , which is unital and generated partial isometries {t i } i∈Σ . Then the partial isometries that generate O Λ obey the following relations:…”

Section: Preliminariesmentioning

confidence: 99%

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Orbit Representations from Linear mod 1 Transformations

Ramos

Martins

Pinto

2012

SIGMA

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Abstract. We show that every point x 0 ∈ [0, 1] carries a representation of a C * -algebra that encodes the orbit structure of the linear mod 1 interval map f β,α (x) = βx + α. Such C * -algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map f β,α . Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every α ∈ [0, 1[ and β ≥ 1.

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Section: Preliminariesmentioning

confidence: 99%

“…This method has also been applied to the context of fractals that arise from affine iterated function systems [10]. Some of these results have been extended to the more general class of Cuntz-Krieger algebras, see [7,13] and subshift C * -algebras [4,11,15] (whose underlying subshift is not necessarily of finite type) in [5].…”

Section: Introductionmentioning

confidence: 99%

Orbit Representations from Linear mod 1 Transformations

Ramos

Martins

Pinto

2012

SIGMA

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Representations of Polynomial Covariance Type Commutation Relations by Linear Integral Operators on $$L_p$$ Over Measure Spaces

Djinja

Silvestrov

Tumwesigye

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Conditions for linear integral operators on over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutation relations and for important classes of polynomial covariance commutation relations associated to arbitrary monomials and to affine functions. Representations of the covariance type commutation relations by integral Volterra operators and integral convolution operators are investigated.

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