COMPACT HOMOMORPHISMS BETWEEN ALGEBRAS OF ANALYTIC-FUNCTIONS

Authors
ARON R GALINDO P LINDSTROM M
Citation
R. Aron et al., COMPACT HOMOMORPHISMS BETWEEN ALGEBRAS OF ANALYTIC-FUNCTIONS, Studia Mathematica, 123(3), 1997, pp. 235-247
Citations number
29
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Studia Mathematica → ACNP
ISSN journal
00393223
Volume
123
Issue
3
Year of publication
1997
Pages
235 - 247
Database
ISI
SICI code
0039-3223(1997)123:3<235:CHBAOA>2.0.ZU;2-I
Abstract
We prove that every weakly compact multiplicative linear continuous ma p from H infinity(D) into H infinity(D) is compact. We also give an ex ample which shows that this is not generally true for uniform algebras . Finally we characterise the spectra of compact composition operators acting on the uniform algebra H infinity(B-E), where B-E is the open unit ball of an infinite-dimensional Banach space E.