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A note on classification of submodules in 
Author(s):
Rongwei
Yang
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2655-2659.
MSC (2000):
Primary 47A13;
Secondary 46E20
Posted:
March 30, 2009
MathSciNet review:
2497478
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Additional information
Abstract:
The Hardy spaces  can be viewed as a module over the polynomial ring ![$ C[z_1,z_2]$](/proc/2009-137-08/S0002-9939-09-09893-1/gif-abstract0/img2.gif) . 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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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