|
Invariant subspaces in Bergman space over the bidisc
Author(s):
David
Redett;
James
Tung
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2425-2430.
MSC (2010):
Primary 47A15
Posted:
March 4, 2010
MathSciNet review:
2607872
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we investigate the doubly commuting condition restricted to invariant subspaces of the Bergman space over the bidisc. This condition was first introduced by V. Mandrekar in the setting of the Hardy space over the bidisc.
References:
-
- 1.
- A. Aleman, S. Richter and C. Sundberg, Beurling's theorem for the Bergman space, Acta. Math. 177 (1996), 275-310. MR 1440934 (98a:46034)
- 2.
- C. Apostol, H. Bercovici, C. Foias and C. Pearcy, Invariant subspaces, dilation theory and the structure of the predual of a dual algebra, J. Funct. Anal. 63 (1985), 369-404. MR 808268 (87i:47004a)
- 3.
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta. Math. 81 (1949), 239-255. MR 0027954 (10:381e)
- 4.
- P. Duren and A. Schuster, Bergman Spaces, Math. Surveys and Monographs, 100, Amer. Math. Soc., Providence, RI, 2004. MR 2033762 (2005c:30053)
- 5.
- V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), 145-148. MR 938659 (90c:32008)
- 6.
- W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 0255841 (41:501)
- 7.
- S. Shimorin, Wold-type decompositions and wandering subspaces for operators close to isometries, J. Reine Angew. Math. 531 (2001), 147-189. MR 1810120 (2002c:47018)
- 8.
- M. Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), 255-262. MR 587496 (83e:47031)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
47A15
Retrieve articles in all Journals with
MSC (2010):
47A15
Additional Information:
David
Redett
Affiliation:
Department of Mathematics, Indiana University-Purdue University Fort Wayne, Fort Wayne, Indiana 46805
Email:
redettd@ipfw.edu
James
Tung
Affiliation:
5701 N. Sheridan Road, Apartment 25M, Chicago, Illinois 60660
Email:
yanchun.tung@gmail.com
DOI:
10.1090/S0002-9939-10-10337-2
PII:
S 0002-9939(10)10337-2
Received by editor(s):
September 8, 2009
Posted:
March 4, 2010
Additional Notes:
This work was done, in part, while the second author was visiting IPFW as a Scholar-in-Residence
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
