ArticleOriginal scientific text

Title

Normal Hilbert modules over the ball algebra A(B)

Authors 1

Affiliations

  1. Department of Mathematics, Fudan University, Shanghai 200433, P.R. China

Abstract

The normal cohomology functor Ext is introduced from the category of all normal Hilbert modules over the ball algebra to the category of A(B)-modules. From the calculation of Ext-groups, we show that every normal C(∂B)-extension of a normal Hilbert module (viewed as a Hilbert module over A(B) is normal projective and normal injective. It follows that there is a natural isomorphism between Hom of normal Shilov modules and that of their quotient modules, which is a new lifting theorem of normal Shilov modules. Finally, these results are applied to the discussion of rigidity and extensions of Hardy submodules over the ball algebra.

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Pages:
1-12
Main language of publication
English
Received
1996-06-20
Accepted
1997-12-09
Published
1999
Exact and natural sciences