Abstract
In this paper we present a wide collection of Banach spaces \(B\) of boundary values on the unit circle around the origin. A common property of the set is that each \(B\) has a countable Schauder basis. In each \({\rm GL}(B)\) we present an open subset \(\tilde{\Omega}(B)\) from which we can construct a solution of the KP hierarchy and we introduce a fiber bundle over \(\tilde{\Omega}(B)\) that yields solutions of the strict KP hierarchy. Finally we show that the set \(\tilde{\Omega}(B)\) can be described by the nonvanishing of a Fredholm determinant. The solutions of the KP hierarchy constructed from \(\tilde{\Omega}(B)\) can be expressed in this Fredholm determinant.
