Operator Theory in the Hardy Space over the Bidisk, III

This paper is a continuation of an effort to build an organized operator theory in H2(D2). It studies self-commutators for certain operator pairs and defines some numerical invariants for submodules. The fringe operator, which captures much of the information of the pairs, is defined in the last section and is used to establish an equality which connects the numerical invariants to traces of the self-commutators.