Polynomially bounded operators and Ext groups

Ferguson, Sarah

doi:10.1090/S0002-9939-96-03340-0

Polynomially bounded operators and Ext groups
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by Sarah H. Ferguson

Proc. Amer. Math. Soc. 124 (1996), 2779-2785

DOI: https://doi.org/10.1090/S0002-9939-96-03340-0

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Abstract:

In this paper, we consider the Ext functor in the category of Hilbert modules over the disk algebra. We characterize the group $\operatorname {Ext}_{A(D)}(K,H)$ as a quotient of operators and explicitly calculate $\operatorname {Ext}_{A(D)}(K, H^{2})$, where $K$ is a weighted Hardy space. We then use our results to give a simple proof of a result due to Bourgain.

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