Polynomially bounded operators and Ext groups

Abstract

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