Transactions of the American Mathematical Society

Author(s): Pamela Gorkin; Raymond Mortini
Journal: Trans. Amer. Math. Soc. 358 (2006), 553-571.
MSC (2000): Primary 47B38; Secondary 47B33, 46J10
Posted: December 28, 2004
Retrieve article in: PDF DVI PostScript

Abstract: We compute norms and essential norms of linear combinations of endomorphisms on uniform algebras.

1.: Richard Aron, Pablo Galindo, and Mikael Lindström, Connected components in the space of composition operators in $H\sp \infty$ functions of many variables, Integral Equations Operator Theory 45 (2003), no. 1, 1-14. MR 2003m:47041
2.: Sheldon Axler and Pamela Gorkin, Sequences in the maximal ideal space of $H\sp \infty$ , Proc. Amer. Math. Soc. 108 (1990), no. 3, 731-740. MR 90h:46087
3.: Joseph A. Cima, Svante Janson, and Keith Yale, Completely continuous Hankel operators on $H\sp \infty$ and Bourgain algebras, Proc. Amer. Math. Soc. 105 (1989), no. 1, 121-125. MR 89g:30065
4.: Joel F. Feinstein and Herbert Kamowitz, Compact endomorphisms of $H\sp \infty(D)$ , Studia Math. 136 (1999), no. 1, 87-90. MR 2001h:46093
5.: Pablo Galindo, T. W. Gamelin, and Mikael Lindström, Composition operators on uniform algebras and the pseudohyperbolic metric, J. Korean Math. Soc. 41 (2004), no. 1, 1-20. MR 2048697
6.: T. W. Gamelin, Homomorphisms of uniform algebras, Recent progress in functional analysis (Valencia, 2000), North-Holland Math. Stud., vol. 189, North-Holland, Amsterdam, 2001, pp. 95-105. MR 2002h:46084
7.: Pamela Gorkin, Raymond Mortini, and Daniel Suárez, Homotopic composition operators on $H\sp \infty(B\sp n)$ , Function spaces (Edwardsville, IL, 2002), Contemp. Math., vol. 328, Amer. Math. Soc., Providence, RI, 2003, pp. 177-188. MR 1990399 (2004i:47047)
8.: Takuya Hosokawa, Keiji Izuchi, and Dechao Zheng, Isolated points and essential components of composition operators on $H\sp \infty$ , Proc. Amer. Math. Soc. 130 (2002), no. 6, 1765-1773. MR 2003d:47033
9.: Herbert Kamowitz, Compact endomorphisms of Banach algebras, Pacific J. Math. 89 (1980), no. 2, 313-325. MR 82c:46063
10.: Udo Klein, Kompakte multiplikative Operatoren auf uniformen Algebren, Mitt. Math. Sem. Giessen 232 (1997), iv+120. MR 99b:47043
11.: Heinz König, Zur abstrakten Theorie der analytischen Funktionen. II, Math. Ann. 163 (1966), 9-17. MR 32:8202
12.: H. L. Royden, Function algebras, Bull. Amer. Math. Soc. 69 (1963), 281-298. MR 26:6817
13.: Carl Toews, Topological components of the set of composition operators in ${H}^\infty({B}_{N})$ , Integral Equations Operator Theory 48 (2004), no. 2, 265-280.
14.: Lixin Zheng, The essential norms and spectra of composition operators on $H\sp \infty$ , Pacific J. Math. 203 (2002), no. 2, 503-510. MR 2003e:47052

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 47B38, 47B33, 46J10

Pamela Gorkin
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
Email: pgorkin@bucknell.edu

Raymond Mortini
Affiliation: Département de Mathématiques, Université de Metz, Ile du Saulcy, F-57045 Metz, France
Email: mortini@poncelet.univ-metz.fr

DOI: 10.1090/S0002-9947-04-03633-5
PII: S 0002-9947(04)03633-5
Received by editor(s): May 14, 2003
Received by editor(s) in revised form: January 25, 2004
Posted: December 28, 2004
Additional Notes: The first author wishes to thank the Université de Metz and Universität Bern for its support during the time this paper was conceived and written. Both authors are grateful to the Mathematisches Forschungsinstitut in Oberwolfach for allowing them to participate in the RIP program.
Copyright of article: Copyright 2004, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(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 2008, American Mathematical Society Privacy Statement		Search the AMS