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On K 0-groups of operator algebras on Banach spaces

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Abstract

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K 0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X 2 is not a sufficient condition of K 0(B(X)) = 0.

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References

  1. Gowers, W. T., Maurey, B., The unconditional basic sequence problem, J. A. M. S., 1993, 6(sn3): 851–874.

    MathSciNet  Google Scholar 

  2. Gowers, W. T., Maurey, B., Banach spaces with small spaces of operators, Math. Ann., 1997, 307: 543–568.

    Article  MathSciNet  Google Scholar 

  3. Lindenstrauss, J., The work of Gowers W. T., Notices of A. M. S., 1999, 46(1): 19–20.

    MathSciNet  Google Scholar 

  4. Maurey, B., Banach spaces with few operators, Handbook of the Geometry of Banach Spaces, Vol. 2, Amsterdam: North-Holland, 2002, 1247-1298.

  5. Zhong, H. J., Significant developments in the structural theory of Banach spaces based on the series of results by Gowers and Maurey, Adv. Math. (in Chinese), 2000, 19(1): 1–18.

    Google Scholar 

  6. Zhong, H. J., Structure of Banach Spaces and Operator Ideals, Beijing: Science Press, 2005.

    Google Scholar 

  7. Johnson, W. B., Lindenstrauss, J., eds., Handbook of the Geometry of Banach Spaces, Vol.1, Amsterdam: Elsevier, 2001.

    Google Scholar 

  8. Zhong, H. J., Chen, D. X., Chen, J. L., Some G-M-type Banach spaces and K-groups of operator algebras on them, Science in China, Ser. A, 2004, 47(3): 372–392.

    MathSciNet  Google Scholar 

  9. Laustsen, N. J., K-theory for algebra of operators on Banach spaces, J. London Math. Soc., 1999, 59(2): 715–728.

    Article  MATH  MathSciNet  Google Scholar 

  10. Ferenczi, V., Quotient hereditarily indecomposable Banach spaces, Canad. J. Math., 1999, 51: 566–581.

    MATH  MathSciNet  Google Scholar 

  11. Li, B. R., Banach Algebra, Beijing: Science Press, 1997.

    Google Scholar 

  12. Casazza, P. G., The Schroeder-Bernstein property for Banach spaces, in Banach Spaces Theory, Contemporary Math. (ed. Lin Bor-L), Vol. 85, A. M. S.: PRI, 1989, 61-78.

  13. Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces I, New York: Springer-Verlag, 1977.

    Google Scholar 

  14. Zsak, A., A Banach space whose operator algebra has K 0-group Q, Proc. London Math. Soc., 2002, 80(3): 747–768.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    Zhang Yunnan, Zhong Huaijie & Su Weigang

Authors
  1. Zhang Yunnan
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  2. Zhong Huaijie
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  3. Su Weigang
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Correspondence to Zhong Huaijie.

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Zhang, Y., Zhong, H. & Su, W. On K 0-groups of operator algebras on Banach spaces. SCI CHINA SER A 49, 233–244 (2006). https://doi.org/10.1007/s11425-005-0042-0

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  • DOI: https://doi.org/10.1007/s11425-005-0042-0

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