C*-ALGEBRAS ASSOCIATED WITH SETS OF SEMIGROUPS OF ISOMETRIES

Let U₀, U₁, …, U_n be a (finite or infinite) sequence of semigroups of isometries which act on the same separable Hilbert space H, n = 1, 2, …, ∞. {U_j} is said to be orthogonal if for all i ≠ j we have

With every such sequence we associate a separable C*-algebra . These C*-algebras , n = 1, 2, …, ∞, are the "continuous time" analogues of the Cuntz C*-algebras , n = 2, 3, …, ∞, in the same sense that the Wiener-Hopf C*-algebra is the continuous time analogue of the Toeplitz C*-algebra. For example, we show that they are nuclear unitless C*-algebras which have no closed nontrivial ideals. Indeed, we show that each is stably isomorphic to one of the spectral C*-algebras which arise in the theory of E₀-semigroups.