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Representations approximating quasirepresentations of amenable groups can depend on the choice of an invariant mean

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In the paper, the dependence of an ordinary representation constructed by some averaging process and approximating a given quasirepresentation of an amenable group on the choice of an invariant mean used in the averaging processes is discussed.

Abstract

In the paper, the dependence of an ordinary representation constructed by some averaging process and approximating a given quasirepresentation of an amenable group on the choice of an invariant mean used in the averaging processes is discussed.

참고문헌 (12)

  1. Shtern A. I., "Quasisymmetry", I, Russian J. Math. Phys, 2(3), pp.353~382 (1994)
  2. Shtern A. I, "Finite-dimensional quasi-representations of connected Lie groups and Mishchenko’s conjecture", J. Math. Sci, 159(5), pp.653~751 (2009)
  3. Grove K, "Jacobi fields and Finsler metrics on a compact Lie groups with an application to differential pinching problems", Math. Ann, 211(1), pp.7~21 (1974)
  4. de la Harpe P, "Representations approch´ees d’un groupe dans une alg´ebre de Banach", Manuscripta Math, 22(3), pp.297~310 (1977)
  5. Shtern A. I., "Norm continuous representations of locally compact groups", Russ. J. Math. Phys, 15(4), pp.552~553 (2008)
  6. Kazhdan D, "On ²-representations", Israel J. Math, 43(4), pp.315~323 (1982)
  7. Faiziev V. A, "Pseudocharacters on free products of semigroups", Funct. Anal. Appl, 21(1), pp.77~79 (1987)
  8. Shtern A. I, "Rigidity and approximation of quasi-representations of amenable groups", Math. Notes, 65(6), pp.760~769 (1999)
  9. Shtern A. I, "On operators in Fr´echet spaces that are similar to isometries", Moscow Univ. Math. Bull, 46(4), pp.47~48 (1991)
  10. Greenleaf F.P, "Invariant means on topological groups and their applications" (1969), Van Nostrand
  11. Shtern A. I., "Almost convergence and its applications to the Fourier–Stieltjes localization", Russian J. Math. Phys, 1(1), pp.115~125 (1993)
  12. Shtern A. I, "A direct proof of a corollary to a theorem of B. E. Johnson", ~

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