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By Edward G. Effros (auth.), Huzihiro Araki, Richard V. Kadison (eds.)

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Extra resources for C*-Algebras and Applications to Physics: Proceedings, Second Japan-USA Seminar, Los Angeles, April 18–22, 1977

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G a group Then there exists a one-to-one correspondence between the class of subgroups of G and the class of intermediate subalgebras faithful normal expectation for all e of G®A B onto of B G@A having a such that e(A(g))=O A(g)iB, by the same association as in Theorem 12. 6. Galois correspondences. a Galois correspondence. Neumann algebra In this section, we shall consider Throughout this section, we shall use a von A, a group G of freely acting automorphisms of and the fixed point algebra B of Neumann subalgebra of of A A containing under B G.

35. M. Nakamura and Z. Takeda, On some elementary properties of the crossed products of von Neumann algebras, Proc. , 34(1958}, 489-494. 36. and , A Galois theory for finite factors, Proc. Japan --Acad. ,36(1960), 258-260. 37. and , On the fundamental theorem of the Galois theory -----for finite factors, Proc. , 36(1960), 313-318. 38. T. Saito, The direct product and the crossed product of rings of operators, Tohoku Math. , 11(1959), 299-304. 39. I. M. Singer, Automorphisms of finite factors, Amer.

E shall need on the tensor products and their duals. , n~l) and in fact, we shall restrict our attention to defining orderings on and the correspondinp: duals (V0Wt, V~vl" in ,7. VG)W 37 References 1. E. M. Alfsen, Comoact Convex Sets and Boundary Integrals, Springer Verlag, Berlin, 1971 2. ", M. A1fsen and F. ~T. Shultz, State spaces of ,Jordan algebras, to appear. 3. lv, B. Arveson, Subalgebras of r,;:--alf'ebras. I, Acta 1'Kath. 123 (1969), 141-224. 4. w. B. Notes on extensions Of C*-algebras, ~rve5on.

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