Proceedings of the American Mathematical Society

Author(s): Valentin Matache
Journal: Proc. Amer. Math. Soc. 127 (1999), 1483-1491.
MSC (1991): Primary 47B38; Secondary 47B10
Posted: January 29, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract: We consider composition operators on Hardy spaces of a half-plane. We mainly study boundedness and compactness. We prove that on these spaces there are no compact composition operators.

1.: C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press Boca Raton, New York, London, Tokyo, 1995. MR 97i:47056
2.: P. L. Duren, Theory of $H^{p}$ Spaces, Academic Press, New York, 1970. MR 42:3552
3.: J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 83g:30037
4.: P. R. Halmos, Measure Theory, Van Nostrand, Princeton, NJ, 1950. MR 11:504d
5.: K. Hoffman, Banach Spaces of Analytic Functions, Englewood Cliffs, NJ, 1962. MR 24:A2844
6.: V. Matache, Composition Operators on $H^{p}$ of the Upper Half-Plane, An. Univ. Timisoara Ser. Stiint. Mat. 27 (1989), 63-66. MR 92k:47063
7.: E. A. Nordgren, Composition Operators in Hilbert Spaces, Hilbert Space Operators, Lecture Notes in Mathematics, vol. 693, Springer-Verlag, New York, Heidelberg, Berlin, 1978, pp. 37-63. MR 80d:47046
8.: J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1993. MR 94k:47049
9.: S. D. Sharma, Compact and Hilbert-Schmidt Composition Operators on Hardy Spaces of the Upper Half-Plane, Acta Sci. Math. (Széged) 46 (1983), 197-202. MR 85g:47032
10.: S. D. Sharma and R. K. Singh, Composition Operators on Hardy Spaces of the Upper Half-Plane, preprint (1996).
11.: R. K. Singh, A Relation Between Composition Operators on $H^{2}({\mathbb{D}})$ and $H^{2}({\Pi ^{+}})$ , Pure Appl. Math. Sci. 1 (1974), 1-5. MR 56:12971
12.: R. K. Singh and S. D. Sharma, Composition Operators on a Functional Hilbert Space, Bull. Austral. Math. Soc. 20 (1979), 377-384. MR 81c:47034
13.: R. K. Singh and S. D. Sharma, Noncompact Composition Operators, Bull. Austral. Math. Soc. 21 (1980), 125-130. MR 81m:47046

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B38, 47B10

Valentin Matache
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142
Address at time of publication: Department of Mathematics, University of Puerto Rico, P. O. Box 9018, Mayagüez, Puerto Rico 00681-9018
Email: matache@math.ukans.edu, matache@math.upr.clu.edu

DOI: 10.1090/S0002-9939-99-05060-1
PII: S 0002-9939(99)05060-1
Keywords: Composition operator, Hardy space, compact operator
Received by editor(s): September 1, 1997
Posted: January 29, 1999
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS