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CROSS COMMUTATORS ON BACKWARD SHIFT INVARIANT SUBSPACES OVER THE BIDISK II

  • Izuchi, Kei Ji ;
  • Izuchi, Kou Hei
  • Received : 2010.09.20
  • Published : 2012.01.01

Abstract

In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [${S_z}^n$, $S_w^*$] = 0 for a positive integer n ${\geq}$ 2. In this case, it holds that ${S_z}^n=cI$ for some $c{\in}\mathbb{C}$. In this paper, it is proved that if [$S_{\varphi}$, $S_w^*$] = 0 and ${\varphi}{\in}H^{\infty}({\Gamma}_z)$, then $S_{\varphi}=cI$ for some $c{\in}\mathbb{C}$.

Keywords

backward shift invariant subspace;invariant subspace;Hardy space;cross commutator

References

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Acknowledgement

Supported by : Japan Society for the Promotion of Science