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C*-Algebra Generated by Mapping Which Has Finite Orbits

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Operator Theory, Operator Algebras and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 242))

Abstract

We consider the C*-subalgebra of the algebra of all bounded operators on Hilbert space of square-summable functions on some countable set. The algebra being investigated is generated by a family of partial isometries. These isometries satisfy the relations defined by a preassigned mapping on the set. It is assumed that the mapping has elements with finite orbits. Under this assumption the algebra we consider contains the subalgebra of compact operators and its quotient algebra is \( \mathbb{Z} \)-graded. We consider the covariant system associated with the quotient algebra and construct the conditional expectation onto the fixed point subalgebra. We prove that the quotient algebra is nuclear and so is the algebra generated by mapping.

Mathematics Subject Classification (2010). Primary 46L99.

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Author information

Authors and Affiliations

  1. Institute of Physics Chair of General Relativity and Gravitation, 18 Kremlyovskaya str., Kazan, 420008, Russia

    Alla Kuznetsova

Authors
  1. Alla Kuznetsova
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Correspondence to Alla Kuznetsova .

Editor information

Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal

    M. Amélia Bastos

  2. Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal

    Amarino Lebre

  3. Departamento de Matemática, Universidade do Algarve, Faro, Portugal

    Stefan Samko

  4. Department of Mathematics, College of William & Mary, Williamsburg, Virginia, USA

    Ilya M. Spitkovsky

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Kuznetsova, A. (2014). C*-Algebra Generated by Mapping Which Has Finite Orbits. In: Bastos, M., Lebre, A., Samko, S., Spitkovsky, I. (eds) Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, vol 242. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0816-3_13

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