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Banach Algebras Generated by N Idempotents and Applications

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Singular Integral Operators and Related Topics

Part of the book series: Operator Theory Advances and Applications ((OT,volume 90))

Abstract

It is well known that for Banach algebras generated by two idempotents and the identity all irreducible representations are of order not greater than two. These representations have been described completely and have found important applications to symbol theory. It is also well known that without additional restrictions on the idempotents these results do not admit a natural generalization to algebras generated by more than two idempotents and the identity. In this paper we describe all irreducible representations of Banach algebras generated by N idempotents which satisfy some additional relations. These representations are of order not greater than N and allow us to construct a symbol theory with applications to singular integral operators.

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Authors and Affiliations

  1. Fakultät für Mathematik, TU Chemnitz-Zwickau, 09107, Chemnitz, Germany

    A. Böttcher, Yu. I. Karlovich & B. Silbermann

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  3. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    N. Krupnik

  4. Mathematisches Institut, Universität Leipzig, Augustusplatz 10 - 11, 04109, Leipzig, Germany

    S. Roch

  5. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA

    I. Spitkovsky

Authors
  1. A. Böttcher
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  2. I. Gohberg
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  3. Yu. I. Karlovich
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  4. N. Krupnik
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  5. S. Roch
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  6. B. Silbermann
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  7. I. Spitkovsky
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Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Israel

    I. Gohberg

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© 1996 Birkhäuser Verlag, Basel/Switzerland

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Böttcher, A. et al. (1996). Banach Algebras Generated by N Idempotents and Applications. In: Böttcher, A., Gohberg, I. (eds) Singular Integral Operators and Related Topics. Operator Theory Advances and Applications, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9040-3_2

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  • DOI: https://doi.org/10.1007/978-3-0348-9040-3_2

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9881-2

  • Online ISBN: 978-3-0348-9040-3

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