Two Inner Sequences Based Invariant Subspaces in H2(D2)

摘要

Let M be a shift invariant subspace in the vector-valued Hardyspace H~2 _E(D). The Beurling-Lax-Halmos theorem says that M can becompletely characterized by B(E)-valued inner function Θ. When E =H~2(D), H~22_E(D) is the Hardy space on the bidisk H~2(D_2). Recently, Qinand Yang (Proc Am Math Soc, 2013) determines the operator valuedinner function Θ(z) for two well-known invariant subspaces in H~2(D~2).This paper generalizes the Θ(z) by Qin and Yang (Proc Am Math Soc,2013) and deal with the structure of M = Θ(z)H~2(D~2) when M isan invariant subspace in H~2(D~2). Unitary equivalence, spectrum of thecompression operator and core operator are studied in this paper.