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A Subnormal Toeplitz Completion Problem

  • Raúl E. CurtoEmail author
  • In Sung Hwang
  • Woo Young Lee
Conference paper
  • 457 Downloads
Part of the Operator Theory: Advances and Applications book series (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.

Keywords

(Block) Toeplitz operators bounded type functions matrix-valued rational functions Halmos’ Problem 5 Abrahamse’s Theorem hyponormal subnormal completion 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Raúl E. Curto
    • 1
    Email author
  • In Sung Hwang
    • 2
  • Woo Young Lee
    • 3
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsSungkyunkwan UniversitySuwonKorea
  3. 3.Department of MathematicsSeoul National UniversitySeoulKorea

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