Journal of the Mathematical Society of Japan

Hulls and kernels from topological dynamical systems and their applications to homeomorphism $C^{*}$ -algebras

Jun TOMIYAMA

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Abstract

For a topological dynamical system Σ=(X,σ) where σ is a homeomorphism in an arbitrary compact Hausdorff space X, we consider the noncommutative hulls and kernels with respect to the action σ in the associated C*- algebra A(Σ). We show that several ideals important for the structure of A(Σ) have the form of such kernels and give topological characterizations of their hulls from the behavior of orbits in the dynamical system.

Article information

Source
J. Math. Soc. Japan, Volume 56, Number 2 (2004), 349-364.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418634

Digital Object Identifier
doi:10.2969/jmsj/1191418634

Mathematical Reviews number (MathSciNet)
MR2048463

Zentralblatt MATH identifier
1064.46054

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 37A55: Relations with the theory of C-algebras [See mainly 46L55] 54H15: Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]

Keywords
Homeomorphism noncommutative hull-kernel crossed product recurrent point periodic point

Citation

TOMIYAMA, Jun. Hulls and kernels from topological dynamical systems and their applications to homeomorphism $C^{*}$ -algebras. J. Math. Soc. Japan 56 (2004), no. 2, 349--364. doi:10.2969/jmsj/1191418634. https://projecteuclid.org/euclid.jmsj/1191418634


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