On C*-algebras Cut down by Closed Projections: Characterizing Elements via the Extreme Boundary
نویسنده
چکیده
Let A be a C*-algebra. Let z be the maximal atomic projection and p a closed projection in A∗∗. It is known that x in A∗∗ has a continuous atomic part, i.e. zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Under some additional conditions, we shall show that if x is uniformly continuous on the set of pure states of A supported by p, or its weak* closure, then pxp has a continuous atomic part, i.e. zpxp = zpap for some a in A.
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تاریخ انتشار 2004