A note on classification of submodules in $H^{2}(D^{2})$
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- by Rongwei Yang PDF
- Proc. Amer. Math. Soc. 137 (2009), 2655-2659 Request permission
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.References
- Xiaoman Chen and Kunyu Guo, Analytic Hilbert modules, Chapman & Hall/CRC Research Notes in Mathematics, vol. 433, Chapman & Hall/CRC, Boca Raton, FL, 2003. MR 1988884, DOI 10.1201/9780203008836
- R. G. Douglas, V. I. Paulsen, C.-H. Sah, and K. Yan, Algebraic reduction and rigidity for Hilbert modules, Amer. J. Math. 117 (1995), no. 1, 75–92. MR 1314458, DOI 10.2307/2375036
- Kunyu Guo and Rongwei Yang, The core function of submodules over the bidisk, Indiana Univ. Math. J. 53 (2004), no. 1, 205–222. MR 2048190, DOI 10.1512/iumj.2004.53.2327
- Keiji Izuchi and Kou Hei Izuchi, Rank-one commutators on invariant subspaces of the Hardy space on the bidisk, J. Math. Anal. Appl. 316 (2006), no. 1, 1–8. MR 2201744, DOI 10.1016/j.jmaa.2005.04.021
- Keiji Izuchi, Takahiko Nakazi, and Michio Seto, Backward shift invariant subspaces in the bidisc. II, J. Operator Theory 51 (2004), no. 2, 361–376. MR 2074186
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Rongwei Yang, On two-variable Jordan blocks, Acta Sci. Math. (Szeged) 69 (2003), no. 3-4, 739–754. MR 2034205
- Rongwei Yang, The core operator and congruent submodules, J. Funct. Anal. 228 (2005), no. 2, 469–489. MR 2175415, DOI 10.1016/j.jfa.2005.06.022
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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2655-2659
- MSC (2000): Primary 47A13; Secondary 46E20
- DOI: https://doi.org/10.1090/S0002-9939-09-09893-1
- MathSciNet review: 2497478