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 GL (B) we present an open subset (B) from which we can construct a solution of the KP hierarchy and we introduce a fiber bundle over (B) that yields solutions of the strict KP hierarchy. Finally we show that the set (B) can be described by the nonvanishing of a Fredholm determinant. The solutions of the KP hierarchy constructed from (B) can be expressed in this Fredholm determinant.
Helminck et al. (Sat,) studied this question.