Inner sequence based invariant subspaces in $H^{2}(D^2)$

Abstract

A closed subspace H2 (D2) is said to be invariant if it is invariant under the Toeplitz operators Tz and Tw. Invariant subspaces of H2 (D2) are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for Σ j 1 - |λj|, where {λj} are zeros of a Blaschke product. © 2007 American Mathematical Society Reverts to public domain 28 years from publication.