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Given a faithful flowon a C ∗ -algebra A, when A is - simple we will show that the closed subalgebra of A consisting of elements with non-negative Arveson spectra is maximal if and only if the crossed product of A byis simple. We will also show how the general case can be reduced to the -simple case, which roughly says that any flow with the above maximality is an extension of a trivial flow by a flow of the above type in the -simple case. We also propose a condition of essential maximality for such closed subalgebras.

MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C*-ALGEBRAS WITH FLOWS

MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C^*-ALGEBRAS WITH FLOWS