Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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FACTORIZATION OF A HILBERT SPACE ON THE BIDISK

  • Yang, Mee-Hyea (Department of Mathematics University of Incheon) ;
  • Hong, Bum-Il (Department of Applied Mathematics Kyung Hee University)
  • Received : 2009.10.15
  • Accepted : 2009.11.13
  • Published : 2009.12.25
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Abstract

Let $S(z_1,z_2),\;S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ be power series with operator coefficients such that $S_(z_1,\;z_2)=S_1(z_1,z_2)S_2(z_1,z_2)$. Assume that the multiplications by $S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ are contractive transformations in H($\mathbb{D}^2,\;\mathcal{C}$). Then the factorizations of spaces $\mathcal{D}(\mathbb{D},\;\tilde{S})$ and $\mathcal{D}(\mathbb{D}^2,\mathcal{S})$ are well-behaved.

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References

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