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In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. In- stead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind inte- gral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels.

A Generalized Collectively Compact Operator Theory with An Application to Integral Equations on Unbounded Domains