An index formula for the two variable Jordan block

Lu, Yufeng; Yang, Yixin; Yang, Rongwei

doi:10.1090/S0002-9939-2010-10497-5

An index formula for the two variable Jordan block
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by Yufeng Lu, Yixin Yang and Rongwei Yang PDF

Proc. Amer. Math. Soc. 139 (2011), 511-520 Request permission

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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