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Complemented invariant subspaces and interpolation sequences
Author(s):
Evgueni
Doubtsov
Journal:
Proc. Amer. Math. Soc.
135
(2007),
393-395.
MSC (2000):
Primary 47A15;
Secondary 30D55, 30H05
Posted:
August 21, 2006
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Abstract:
It is shown that the invariant subspace of the Bergman space  of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in  .
References:
-
- 1.
- Cohn W.S., Complemented invariant subspaces of
 , and the Hahn-Banach extension property, Proc. Amer. Math. Soc. 102 (1988), no. 1, 121-124. MR 0915728 (88k:46063) - 2.
- Duren P., Schuster A., Bergman spaces, Mathematical Surveys and Monographs, vol. 100, Amer. Math. Soc., Providence, RI, 2004. MR 2033762 (2005c:30053)
- 3.
- Hedenmalm H., Korenblum B., Zhu K., Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York,
2000. MR 1758653 (2001c:46043) - 4.
- Korenblum B., Zhu K., Complemented invariant subspaces in Bergman spaces, J. London Math. Soc. (2) 71 (2005), no. 2, 467-480. MR 2122439 (2006a:46031)
- 5.
- Zhu K.H., Interpolating sequences for the Bergman space, Michigan Math. J. 41 (1994), no. 1, 73-86. MR 1260609 (94m:46045)
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Additional Information:
Evgueni
Doubtsov
Affiliation:
St. Petersburg Department, V.A. Steklov Institute of Mathematics, Fontanka 27, 191023 St. Petersburg, Russia
Email:
dubtsov@pdmi.ras.ru
DOI:
10.1090/S0002-9939-06-08472-3
PII:
S 0002-9939(06)08472-3
Keywords:
Bergman space,
Hardy space,
invariant subspace
Received by editor(s):
August 10, 2005
Received by editor(s) in revised form:
August 22, 2005
Posted:
August 21, 2006
Additional Notes:
This paper was written while the author enjoyed the hospitality of the Chalmers University of Technology.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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