Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/gleason-parts-and-closed-ideals-in-douglas-algebras-A0TkhBYCJt
References (27)
-
S. Axler, P. Gorkin (1984)
Divisibility in Douglas algebras.Michigan Mathematical Journal, 31
-
K. Izuchi (1994)
Interpolating Blaschke Products and Factorization TheoremsJournal of The London Mathematical Society-second Series, 50
-
R. Mortini (1985)
Finitely generated closed ideals inH∞Archiv der Mathematik, 45
-
P. Gorkin, K. Izuchi, R. Mortini (2000)
Higher Order Hulls in H∞, IIJournal of Functional Analysis, 177
-
S. Chang (1977)
Structure of Subalgebras Between L ∞ and H ∞ -
(2004)
The structure of the maximal ideal space of H∞ -
P. Gorkin, R. Mortini (2005)
Countably generated prime ideals in H∞Mathematische Zeitschrift, 251
-
P. Gorkin, R. Mortini (1991)
Interpolating Blaschke products and factorization in Douglas algebras.Michigan Mathematical Journal, 38
-
Z. Nehari (1950)
Bounded analytic functionsBulletin of the American Mathematical Society, 57
-
K. Hoffman (1967)
Bounded Analytic Functions and Gleason PartsAnnals of Mathematics, 86
-
P Gorkin, K Izuchi, R Mortini (2000)
Higher order hulls in $$H^\infty $$ H ∞ IIJ. Funct. Anal., 177
-
(1976)
Subalgebras of L∞ containing H∞ -
D. Sarason (1973)
Algebras of functions on the unit circleBulletin of the American Mathematical Society, 79
-
S-Y Chang (1977)
Structure of subalgebras between $$L^{\infty }$$ L ∞ and $$H^{\infty }$$ H ∞Trans. Am. Math. Soc., 227
-
K. Izuchi, Y. Izuchi (2013)
Gleason parts and countably generated closed ideals inTransactions of the American Mathematical Society, 365
-
D Sarason (1978)
Function Theory on the Unit Circle, Notes for Lecture note -
S. Chang (1976)
A characterization of douglas subalgebrasActa Mathematica, 137
-
M. Nimchek (1996)
Banach spaces of analytic functions -
J. Bourgain (2017)
ON FINITELY GENERATED CLOSED IDEALS IN H ° ° ( D ) -
D. Sarason (1978)
Function theory on the unit circle -
(2002)
Estimates in the corona theorem and ideals of H∞: a problem of T -
K. Izuchi, Y. Izuchi (2010)
Factorization of Blaschke products and primary ideals in HJournal of Functional Analysis, 259
-
C Guillory, K Izuchi, D Sarason (1984)
Interpolating Blaschke products and division in Douglas algebrasProc. R. Ir. Acad. Sect. A, 84
-
D Marshall (1976)
Subalgebras of $$L^\infty $$ L ∞ containing $$H^\infty $$ H ∞Acta Math., 137
-
K. Izuchi, Y. Izuchi (2011)
Factorization of Blaschke products and ideal theory in HJournal of Functional Analysis, 260
-
R. Mortini (1997)
On an example of J. Bourgain on closures of finitely generated idealsMathematische Zeitschrift, 224
-
S Treil (2002)
Estimates in the corona theorem and ideals of $$H^\infty $$ H ∞ : a problem of T. WolffJ. Anal. Math., 87
- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-015-0136-9
- Publisher site
- See Article on Publisher Site
Abstract
Recently, the study of the structure of closed ideals in $$H^{\infty }$$ H ∞ whose zero sets are contained in G, the union set of non-trivial Gleason parts, has progressed remarkably. We generalize these results to closed ideals in Douglas algebras A. For non-zero functions $$f_1,f_2,\ldots ,f_n$$ f 1 , f 2 , … , f n in A, $$I=\sum ^n_{j=1}f_j A$$ I = ∑ j = 1 n f j A is an ideal (may not be closed) in A. We also show that if I is closed in A and its common zero set is contained in G, then $$I=b A$$ I = b A for a Carleson–Newman Blaschke product b.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Aug 4, 2015