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A Subnormal Toeplitz Completion Problem

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Operator Theory in Harmonic and Non-commutative Analysis

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 240))

Abstract

We give a brief survey of subnormality and hyponormality of Toeplitz operators on the vector-valued Hardy space of the unit circle. We also solve the following subnormal Toeplitz completion problem: Complete the unspecified rational Toeplitz operators (i.e., the unknown entries are rational Toeplitz operators) of the partial block Toeplitz matrix

$$ G: = \left[ \begin{array}{ccc} {{T_{\overline {{\omega _1}} }}}&? \\ ? &{{T_{\overline {{\omega _2}} }}} \end{array} \right]({\omega _1}\,and\,{\omega _2}\,\text{are finite Blaschke products)} $$

to make G subnormal.

Mathematics Subject Classification (2010). Primary 47B20, 47B35.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Raúl E. Curto

  2. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea

    In Sung Hwang

  3. Department of Mathematics, Seoul National University, Seoul, 151-742, Korea

    Woo Young Lee

Authors
  1. Raúl E. Curto
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  2. In Sung Hwang
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  3. Woo Young Lee
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Corresponding author

Correspondence to Raúl E. Curto .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, Virginia, USA

    Joseph A. Ball

  2. Department of Mathematics, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kingdom

    Michael A. Dritschel

  3. Department of Mathematics, University of Auckland, Auckland, New Zealand

    A.F.M. ter Elst

  4. Mathematical Sciences Institute, Université Lille 1Villeneuve d'Ascq, France and The Australian National University, Canberra, Aust Capital Terr, Australia

    Pierre Portal

  5. School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

    Denis Potapov

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Curto, R.E., Hwang, I.S., Lee, W.Y. (2014). A Subnormal Toeplitz Completion Problem. In: Ball, J., Dritschel, M., ter Elst, A., Portal, P., Potapov, D. (eds) Operator Theory in Harmonic and Non-commutative Analysis. Operator Theory: Advances and Applications, vol 240. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-06266-2_5

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