Abstract
The Hochschild and (periodic) cyclic homology of Banach algebras are either trivial or not interesting, see Connes [2], [4], [6]. To correct this deficiency, Connes [3] had produced the entire cyclic cohomology (see also [4], [6], [5]). The entire cyclic cochains are elements of the infinite product (b,B) cohomology bi-complex which satisfy a certain bidegree asymptotic growth condition. The entire cyclic cohomology is a natural target for the asymptotic Chern character of θ-summable Fredholm modules.
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