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Hankel Type Operators, Bourgain Algebras, and Isometries

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Recent Developments in Operator Theory and Its Applications

Part of the book series: Operator Theory Advances and Applications ((OT,volume 87))

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Abstract

Isometries and the complete continuity of Hankel type operators together with certain known Bourgain algebras are used to give a simple proof of the Poincaré theorem concerning the biholomorphic inequivalence of the unit ball and the unit polydisc in C n.

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References

  1. J. Cima, K. Stroethoff and K. Yale, Bourgain algebras on the unit disk, Pacific J. Math. 160 (1993), 27–41.

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  2. J. Cima and R. Timoney, The Dunford-Pettis property for certain planar uniform algebras, Michigan Math. J. 34 (1987), 99–104.

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  3. K. Izuchi, Bourgain algebras of the disk, polydisk and ball algebras, Duke Math. J. 66 (1992), 503–519.

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  4. W. Rudin, Function Theory in the Polydiscs, Benjamin, New York-Amsterdam, 1969.

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  5. K. Yale, Bourgain algebras, pp. 413–422 in “Proceedings Conference on Function Spaces” (edited by K. Jarosz), Lecture Notes in Pure and Appl. Math., Vol. 136, Marcel Dekker, 1992.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Montana, Missoula, Montana, USA

    T. Tonev & K. Yale

Authors
  1. T. Tonev
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  2. K. Yale
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1NA, Canada

    P. Lancaster

  3. Department of Applied Mathematics and Institute of Industrial Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada

    P. N. Shivakumar

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Tonev, T., Yale, K. (1996). Hankel Type Operators, Bourgain Algebras, and Isometries. In: Gohberg, I., Lancaster, P., Shivakumar, P.N. (eds) Recent Developments in Operator Theory and Its Applications. Operator Theory Advances and Applications, vol 87. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9035-9_20

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  • DOI: https://doi.org/10.1007/978-3-0348-9035-9_20

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9878-2

  • Online ISBN: 978-3-0348-9035-9

  • eBook Packages: Springer Book Archive

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