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An index formula for the two variable Jordan block


Authors: Yufeng Lu, Yixin Yang and Rongwei Yang
Journal: Proc. Amer. Math. Soc. 139 (2011), 511-520
MSC (2010): Primary 47A13; Secondary 46E20
DOI: https://doi.org/10.1090/S0002-9939-2010-10497-5
Published electronically: July 13, 2010
MathSciNet review: 2736334
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Abstract: On Hardy space $ H^2(\mathbb{D}^2)$ over the bidisk, let $ (S_z,S_w)$ be the compression of the pair $ (T_z,T_w)$ to the quotient module $ H^2(\mathbb{D}^2)\ominus M$. In this paper, we obtain an index formula for $ (S_z,S_w)$ when it is Fredholm. It is also shown that the evaluation operator $ L(0)$ is compact on a Beurling type quotient module if and only if the corresponding inner function is a finite Blaschke product in $ w$.


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Additional Information

Yufeng Lu
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
Email: lyfdlut1@yahoo.com.cn

Yixin Yang
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
Email: yangyx314272@yahoo.com.cn

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

DOI: https://doi.org/10.1090/S0002-9939-2010-10497-5
Keywords: Index formula, two variable Jordan block, evaluation operator, Hardy space over bidisk
Received by editor(s): December 21, 2009
Received by editor(s) in revised form: March 5, 2010
Published electronically: July 13, 2010
Additional Notes: This research was supported by NSFC, grants no. 10671028 and 10971020
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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