# Normal Hilbert modules over the ball algebra A(B)

Studia Mathematica (1999)

- Volume: 135, Issue: 1, page 1-12
- ISSN: 0039-3223

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topGuo, Kunyu. "Normal Hilbert modules over the ball algebra A(B)." Studia Mathematica 135.1 (1999): 1-12. <http://eudml.org/doc/216640>.

@article{Guo1999,

abstract = {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.},

author = {Guo, Kunyu},

journal = {Studia Mathematica},

keywords = {normal cohomology functor; normal Hilbert modules; ball algebra; normal Shilov modules; quotients modules},

language = {eng},

number = {1},

pages = {1-12},

title = {Normal Hilbert modules over the ball algebra A(B)},

url = {http://eudml.org/doc/216640},

volume = {135},

year = {1999},

}

TY - JOUR

AU - Guo, Kunyu

TI - Normal Hilbert modules over the ball algebra A(B)

JO - Studia Mathematica

PY - 1999

VL - 135

IS - 1

SP - 1

EP - 12

AB - 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.

LA - eng

KW - normal cohomology functor; normal Hilbert modules; ball algebra; normal Shilov modules; quotients modules

UR - http://eudml.org/doc/216640

ER -

## References

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