Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:49:57.216Z Has data issue: false hasContentIssue false
  • English
  • Français

DIFFERENCES OF COMPOSITION OPERATORS ON THE BLOCH SPACE IN THE POLYDISC

Part of: Holomorphic mappings and correspondences Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  17 April 2009

ZHONG-SHAN FANG  and
ZE-HUA ZHOU
ZHONG-SHAN FANG
Affiliation:
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, PR China (email: fangzhongshan@yahoo.com.cn)
ZE-HUA ZHOU*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: zehuazhou2003@yahoo.com.cn)
*
✉For correspondence; e-mail: zehuazhou2003@yahoo.com.cn
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.

Let φ and ψ be holomorphic self-maps of the unit polydisc Un in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ−Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized.

Keywords

essential normcompact differencecomposition operatorBloch spacepolydiscs

MSC classification

Secondary: 47B38: Operators on function spaces (general) 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels) 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32A38: Algebras of holomorphic functions 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 47B33: Composition operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 465 - 471
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The second author was supported in part by the National Natural Science Foundation of China (Grant Nos. 10671141, 10371091).

References

[1] Gorkin, P. and MacCluer, B. D., ‘Essential norms of composition operators’, Integral Equations Operator Theory 48 (2004), 27–40.CrossRefGoogle Scholar
[2] Hosokawa, T. and Ohno, S., ‘Topologicial structures of the set of composition operators on the Bloch space’, J. Math. Anal. Appl. 34 (2006), 736–748.CrossRefGoogle Scholar
[3] Hosokawa, T. and Ohno, S., ‘Differences of composition operators on the Bloch space’, J. Operator. Theory 57 (2007), 229–242.Google Scholar
[4] Timoney, R., ‘Bloch functions in several complex variables, I’, Bull. London Math. Soc. 12(37) (1980), 241–267.CrossRefGoogle Scholar
[5] Timoney, R., ‘Bloch functions in several complex variables, II’, J. Reine Angew. Math. 319 (1980), 1–22.Google Scholar
[6] Toews, C., ‘Topological components of the set of composition operators on H ∞(B N)’, Integral Equations Operator Theory 48 (2004), 265–280.CrossRefGoogle Scholar