  In this work characterizations of Fredholm pairs and chains of Hilbert space
operators are given. Following a well-known idea of several variable operator
theory in Hilbert spaces, the aforementioned objects are characterized in terms
of Fredholm linear and bounded maps. Furthermore, as an application of the main
results of this work, direct proofs of the stability properties of Fredholm
pairs and chains in Hilbert spaces are obtained.

Functional Analysis