Normal Hilbert modules over the ball algebra A(B)
Studia Mathematica, Tome 135 (1999) no. 1, pp. 1-12
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_sm_135_1_1_12,
author = {Kunyu Guo},
title = {Normal {Hilbert} modules over the ball algebra {A(B)}},
journal = {Studia Mathematica},
pages = {1--12},
publisher = {mathdoc},
volume = {135},
number = {1},
year = {1999},
doi = {10.4064/sm-135-1-1-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-135-1-1-12/}
}
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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