Nombre de valeurs propres d'un opérateur elliptique et polynôme de Hilbert-Samuel
The normal cohomology functor 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 -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...
Relations between different extensions of Toeplitz operators are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.