A Perturbation Theory for Core Operators of Hilbert-Schmidt Submodules

Abstract

We discuss a perturbation theory for core operators of HilbertSchmidt submodules in the Hardy space over the bidisk. It is shown that eigenvalues of core operators perturbed by automorphisms of the bidisk have a certain continuity, and also we show that the family of eigenspaces of simple eigenvalues has a local cross section.Mathematics Subject Classification (2010). Primary 47B32; Secondary 47B35.

Rudin's Submodules of $H^2(\mathbb{D}^2)$

“…Here The sequence of Blaschke products as defined above is called the Rudin sequence, and the submodule S Φ as defined above is called the Rudin submodule corresponding to the Rudin sequence Φ. These submodules are also called inner sequence based invariant subspaces of H 2 (D 2 ), and was studied by M. Seto and R. Yang [12], Seto [9,10,11] and Izuchi et al [5].…”