Geodesic
Normal Hilbert modules over the ball algebra A(B)
Studia Mathematica, Tome 135 (1999) no. 1, pp. 1-12

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The normal cohomology functor $Ext_ℵ$ 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 $Ext_ℵ$-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. 
Kunyu Guo. Normal Hilbert modules over the ball algebra A(B). Studia Mathematica, Tome 135 (1999) no. 1, pp. 1-12. doi: 10.4064/sm-135-1-1-12
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