INFINITE SEQUENCES OF INNER FUNCTIONS AND SUBMODULES IN H-2(D-2)

摘要

We deal with infinite sequences of inner functions {q(j)}(j) >= 0 with the property that q(j) is divisible by q(j+1). It is shown that these sequences have a close relation to the module structure of the Hardy space over the bidisk. Commutators, Hilbert-Schmidt norms and spectra of operators related to the module structure will be calculated exactly.