STRICTLY CYCLIC INCIDENCE OPERATOR-ALGEBRAS

We introduce Hilbert algebras I(P, w) as analogues of the combinatoria l incidence algebras of Doubilet, Rota and Stanley. This leads to inte resting Banach algebra contexts in which to view certain important com binatorial functions such as the zeta and Mobius functions. The automo rphisms and derivations of these Hilbert algebras are completely descr ibed. The algebras I(P, w) are used to construct a broad new class of reflexive strictly cyclic operator algebras on Hilbert space.