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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on classification of submodules in $ H^{2}(D^{2})$


Author: Rongwei Yang
Journal: Proc. Amer. Math. Soc. 137 (2009), 2655-2659
MSC (2000): Primary 47A13; Secondary 46E20
Published electronically: March 30, 2009
MathSciNet review: 2497478
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Abstract: The Hardy spaces $ H^{2}(D^{2})$ can be viewed as a module over the polynomial ring $ C[z_1,z_2]$. Based on a study of core operator, a new equivalence relation for submodules, namely congruence, was introduced. This paper gives a classification of congruent submodules by the rank of core operators.


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Additional Information

Rongwei Yang
Affiliation: Department of Mathematics and Statistics, The State University of New York at Albany, Albany, New York 12222
Email: ryang@@math.albany.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09893-1
PII: S 0002-9939(09)09893-1
Keywords: Core operator, congruence, Hardy space, submodules
Received by editor(s): September 9, 2008
Published electronically: March 30, 2009
Additional Notes: This work is supported in part by a grant from the National Science Foundation (DMS 0500333).
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.