Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T23:37:44.657Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted composition operators on the Bloch space

Published online by Cambridge University Press:  17 April 2009

Shûichi Ohno  and
Ruhan Zhao
Shûichi Ohno
Affiliation:
Department of Mathematics, Nippon Institute of Technology, 4–1 Gakuendai, MiyashiroMinami-Saitama 345–8501, Japan e-mail: [email protected]
Ruhan Zhao
Affiliation:
Department of Mathematical Sciences, University of Montana, Missoula, MT 59812United States of America e-mail: [email protected]
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.

We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 177 - 185
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Arazy, J., Multipliers, of Bloch functions (University of Haifa Mathematics Publication Series 54, 1982).Google Scholar
[2]Brown, L. and Shields, A.L., ‘Multipliers and cyclic vectors in the Bloch space’, Michigan Math. J. 38 (1991), 141–146.CrossRefGoogle Scholar
[3]Cowen, C.C. and MacCluer, B.D., Composition operators on spaces of analytic functions (CRC Press, Boca Raton, 1995).Google Scholar
[4]Madigan, K. and Matheson, A., ‘Compact composition operators on the Bloch space’, Trans. Amer. Math. Soc. 347 (1995), 2679–2687.CrossRefGoogle Scholar
[5]Shapiro, J.H., Composition operators and classical function theory (Springer-Verlag, Berlin, Heidelberg, New York, 1993).CrossRefGoogle Scholar
[6]Zhu, K., ‘Multipliers of BMO in the Bergman metric with applications to Toeplitz operators’, J. Funct. Anal. 87 (1989), 31–50.CrossRefGoogle Scholar
[7]Zhu, K., Operator theory in function spaces (Marcel Dekker, New York, 1990).Google Scholar