We continue our recent efforts to exploit the notion ofa unitary isotope to study convex combinations of unitaries in an arbitraryJB*-algebra. Exact analogues of C*-algebraic results, due toR. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved forgeneral JB*-algebras. We show that if a contraction in aJB*-algebra is a convex combination of n unitaries, then it is also a mean of n unitaries. This generalizes a well known theorem of Kadison andPedersen. Our methods also provide alternative proofs of other results forC*-algebras.
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机译：我们将继续努力开发efforts同位素的概念，以研究任意JB *-代数中unit的凸组合。由于R，C *代数结果的精确类似物。 V. Kadison，C。L. Olsen和G. K. Pedersen被证明是一般的JB *-代数。我们证明，如果aJB *-代数中的收缩是n个aries的凸组合，那么它也是n个aries的均值。这概括了卡迪森和佩德森的一个著名定理。我们的方法还为C *代数提供了其他结果的替代证明。
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