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A dilation theorem for $ \cdot $-preserving maps of $ \mathcal{C}^*$-algebras

Author: L. Terrell Gardner
Journal: Proc. Amer. Math. Soc. 73 (1979), 341-345
MSC: Primary 46L05
MathSciNet review: 518516
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Abstract: A linear map of a (unital) $ {\mathcal{C}^\ast}$-algebra into a $ {\mathcal{C}^\ast}$-algebra, which preserves the absolute value, is analyzed as the composition of a (unital) $ ^\ast$-homomorphism into a usually larger target algebra, followed by a suitable multiplication $ x \mapsto xb = {b^{1/2}}x{b^{1/2}}$.

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

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1957. MR 0094722 (20:1234)
  • [2] I. Kaplansky, A theorem on rings of operators, Pacific J. Math. 1 (1951), 227-232. MR 0050181 (14:291a)
  • [3] S. Sherman, The second adjoint of a $ {\mathcal{C}^\ast}$-algebra, Proceedings of the International Congress of Mathematicians, Amer. Math. Soc., Providence, R. I., 1952, p. 470.
  • [4] Jan A. Van Casteren, A characterization of $ {\mathcal{C}^\ast}$-subalgebras, Proc. Amer. Math. Soc. 72 (1978), 54-56. MR 503530 (81h:46069)
  • [5] R. V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math. (3) 56 (1952), 494-503. MR 0051442 (14:481c)

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Keywords: $ {\mathcal{C}^\ast}$-algebra, positive map, absolute value, dilation
Article copyright: © Copyright 1979 American Mathematical Society

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