Invariant subspaces in Bergman space over the bidisc
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- by David Redett and James Tung PDF
- Proc. Amer. Math. Soc. 138 (2010), 2425-2430 Request permission
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
- A. Aleman, S. Richter, and C. Sundberg, Beurling’s theorem for the Bergman space, Acta Math. 177 (1996), no. 2, 275–310. MR 1440934, DOI 10.1007/BF02392623
- C. Apostol, H. Bercovici, C. Foias, and C. Pearcy, Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I, J. Funct. Anal. 63 (1985), no. 3, 369–404. MR 808268, DOI 10.1016/0022-1236(85)90093-X
- Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
- Peter Duren and Alexander Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762, DOI 10.1090/surv/100
- V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), no. 1, 145–148. MR 938659, DOI 10.1090/S0002-9939-1988-0938659-7
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Sergei Shimorin, Wold-type decompositions and wandering subspaces for operators close to isometries, J. Reine Angew. Math. 531 (2001), 147–189. MR 1810120, DOI 10.1515/crll.2001.013
- Marek Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), no. 3, 255–262. MR 587496, DOI 10.4064/ap-37-3-255-262
Additional Information
- David Redett
- Affiliation: Department of Mathematics, Indiana University-Purdue University Fort Wayne, Fort Wayne, Indiana 46805
- MR Author ID: 751935
- Email: redettd@ipfw.edu
- James Tung
- Affiliation: 5701 N. Sheridan Road, Apartment 25M, Chicago, Illinois 60660
- Email: yanchun.tung@gmail.com
- Received by editor(s): September 8, 2009
- Published electronically: 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 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2425-2430
- MSC (2010): Primary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-10-10337-2
- MathSciNet review: 2607872