Quotient modules for some Hilbert modules over the bidisk

In this paper, N ψ -type quotient modules H 2 (T n )/K of the Hardy module on polydisc are defined, where K is the submodule generated by {z 1 − ψ(z k ), 2 ≤ k ≤ n} for a finite Blaschke product. Alternative characterizations are given and an orthonormal basis is constructed. Then we show that the self-commutators and cross-commutators are in trace class, self-commutators are Hilbert-Schmidt. Moreover, the traces and the Hilbert-Schmidt norms are given, respectively.

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Quotient modules for some Hilbert modules over the bidisk

Abstract: In this note, we will prove the essential normality of some type of quotient Hilbert modules over the bidisk. Moreover, we will study some properties of the compression of the multiplication operators to the quotient Hilbert modules.

Cited by 2 publications

References 13 publications

Essentially normal Hilbert modules and K-homology IV: Quasi-homogenous quotient modules of Hardy module on the polydisks

Essentially normal Hilbert modules and K-homology IV: Quasi-homogenous quotient modules of Hardy module on the polydisks

$$N_{\psi }$$-Type Quotient Modules in $$H^{2}({\mathbb {D}}^{n})$$

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