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On mean ergodic convergence in the Calkin algebras


Authors: March T. Boedihardjo and William B. Johnson
Journal: Proc. Amer. Math. Soc. 143 (2015), 2451-2457
MSC (2010): Primary 46B08, 47A35, 47B07
DOI: https://doi.org/10.1090/S0002-9939-2015-12432-X
Published electronically: January 21, 2015
MathSciNet review: 3326027
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Abstract: In this paper we give a geometric characterization of mean ergodic convergence in the Calkin algebras for Banach spaces that have the bounded compact approximation property.


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

  • [1] J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839-873. MR 0005790 (3,208c)
  • [2] Joe Diestel, Hans Jarchow, and Andrew Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR 1342297 (96i:46001)
  • [3] Nelson Dunford, Spectral theory. I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185-217. MR 0008642 (5,39c)
  • [4] I. S. Èdelšteĭn and P. Wojtaszczyk, On projections and unconditional bases in direct sums of Banach spaces, Studia Math. 56 (1976), no. 3, 263-276. MR 0425585 (54 #13539)
  • [5] Israel Gohberg, Seymour Goldberg, and Marinus A. Kaashoek, Classes of linear operators. Vol. I, Operator Theory: Advances and Applications, vol. 49, Birkhäuser Verlag, Basel, 1990. MR 1130394 (93d:47002)
  • [6] Michael Lin, On the uniform ergodic theorem, Proc. Amer. Math. Soc. 43 (1974), 337-340. MR 0417821 (54 #5869)
  • [7] Joram Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. No. 48 (1964), 112 pp. MR 0179580 (31 #3828)
  • [8] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92, Springer-Verlag, Berlin, 1977. MR 0500056 (58 #17766)
  • [9] Mostafa Mbekhta and Jaroslav Zemánek, Sur le théorème ergodique uniforme et le spectre, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 12, 1155-1158 (French, with English and French summaries). MR 1257230 (95b:47010)
  • [10] Heydar Radjavi and Peter Rosenthal, Invariant subspaces, 2nd ed., Dover Publications Inc., Mineola, NY, 2003. MR 2003221 (2004e:47010)

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Additional Information

March T. Boedihardjo
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: march@math.tamu.edu

William B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12432-X
Keywords: Mean ergodic convergence, Calkin algebra, essential maximality, essential norm, compact approximation property.
Received by editor(s): March 18, 2013
Received by editor(s) in revised form: December 7, 2013, and December 18, 2013
Published electronically: January 21, 2015
Additional Notes: The first author was supported in part by the N. W. Naugle Fellowship and the A. G. & M. E. Owen Chair in the Department of Mathematics, Texas A & M University
The second author was supported in part by NSF DMS-1301604.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society

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