Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-25T02:25:04.073Z Has data issue: false hasContentIssue false
  • English
  • Français

A HYPONORMAL TOEPLITZ COMPLETION PROBLEM

Published online by Cambridge University Press:  25 February 2013

IN SUNG HWANG  and
AN HYUN KIM
IN SUNG HWANG
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea e-mail: ihwang@skku.edu
AN HYUN KIM
Affiliation:
Department of Mathematics, Changwon National University, Changwon 641–773, Korea e-mail: ahkim@changwon.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the following ‘Toeplitz completion’ problem: Complete the unspecified analytic Toeplitz entries of the partial block Toeplitz matrix

$\begin{linenomath}A:=\begin{bmatrix} T_{\overline\psi_1}& ?\\[4pt]\T_{\overline\psi_2} \end{bmatrix}\end{linenomath}$
to make A hyponormal, where ψi∈H∞ is a non-constant rational function for i=1,2.

Keywords

47A2047B2047B35

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 1 - 8
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Abrahamse, M. B., Subnormal Toeplitz operators and functions of bounded type, Duke Math. J. 43 (1976), 597–604.Google Scholar
2.Cowen, C., Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), 809–812.CrossRefGoogle Scholar
3.Curto, R. E., Hwang, I. S. and Lee, W. Y., Hyponormality and subnormality of block Toeplitz operators, Adv. Math. 230 (2012), 2094–2151.Google Scholar
4.Douglas, R. G., Banach algebra techniques in the theory of Toeplitz operators, CBMS 15 (Amer. Math. Soc., Providence, RI, 1973).CrossRefGoogle Scholar
5.Gu, C., Hendricks, J. and Rutherford, D., Hyponormality of block Toeplitz operators, Pacific J. Math. 223 (2006), 95–111.Google Scholar
6.Gu, C. and Shapiro, J. E., Kernels of Hankel operators and hyponormality of Toeplitz operators, Math. Ann. 319 (2001), 553–572.Google Scholar
7.Hwang, I. S. and Lee, W. Y., Hyponormal Toeplitz operators with rational symbols, J. Operator Theory 56 (2006), 47–58.Google Scholar
8.Nakazi, T. and Takahashi, K., Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Am. Math. Soc. 338 (1993), 753–769.CrossRefGoogle Scholar
9.Peller, V. V., Hankel operators and their applications (Springer, New York, 2003).Google Scholar