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Acta Mathematica Vietnamica

Mixed invariant subspaces over the bidisk II

Kou Hei Izuchi , icon-email Kei Ji Izuchi

Abstract

For a mixed invariant subspace N of H2 under Tz and Tw, in the previous paper we studied the case rank[Vz,Vw]=1 and either dim(NzN)=0 or 1. In this paper, we study the structure of N satisfying rank[Vz,Vw]=1 and dim(NzN)=2. Our study is deeply concerned with the structure of nonextreme points in the closed unit ball of the space of one variable bounded analytic functions.