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Ideal preserving automorphisms of postliminary $ C\sp \ast$-algebras

Author: George A. Elliott
Journal: Proc. Amer. Math. Soc. 27 (1971), 107-109
MSC: Primary 46.65
MathSciNet review: 0268686
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Abstract: E. C. Lance has shown that an automorphism of a separable postliminary $ {C^ \ast }$-algebra which preserves closed two-sided ideals is universally weakly inner. This note extends Lance's result to the nonseparable case.

References [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les $ {C^ \ast }$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [2] R. V. Kadison and J. R. Ringrose, Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 32-63. MR 34 #6552. MR 0206735 (34:6552)
  • [3] E. C. Lance, Automorphisms of postliminal $ {C^ \ast }$-algebras, Pacific J. Math. 23 (1967), 547-555. MR 36 #3133. MR 0220066 (36:3133)

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Keywords: Postliminary $ {C^ \ast }$-algebra, ideal preserving automorphism, universally weakly inner automorphism, continuous field of Hilbert spaces, associated continuous field of elementary $ {C^ \ast }$-algebras
Article copyright: © Copyright 1971 American Mathematical Society

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