Skip to main content
Log in

Some G-M-type Banach spaces and K-groups of operator algebras on them

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

By providing several new varieties of G-M-type Banach spaces according to decomposable and compoundable properties, this paper discusses the operator structures of these spaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces through calculation of the K-groups of the operator ideals contained in the class of Riesz operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gowers, W. T., Maurey, B., The unconditional basic sequence problem, J.A.M.S., 1993, 6(3): 851–874.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Google Scholar 

  5. Zhong, H. J., Singnificant 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. Blackadar, B., K-theory for Operator Algebras, New York: Springer-Verlag, 1986.

    MATH  Google Scholar 

  7. Li, B. R., Banach Algebras (in Chinese), Beijing: Academic Press, 1992.

    Google Scholar 

  8. Zsak, A., A Banach space whose operator algebra has K0-group Q, Proc. London Math. Soc., 2002, 84(3): 747–768.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  11. Zhong, H. J., On the Gowers-Maurey spaces and their conjugate spaces, Chinese Science Bulletin, 1997, 42(1): 14–16.

    Article  MATH  MathSciNet  Google Scholar 

  12. Pietsch, A., Operator Ideals, Berlin: DVW, 1980.

    MATH  Google Scholar 

  13. Caradus, S. R., Pfaffenberger, W. E., Yood, B., Calkin Algebras and Algebras of Operators on Banach Spaces, New York: Marcel Dekker, 1974.

    MATH  Google Scholar 

  14. Argyros, S. A., Felouzis, V., Interpolating hereditarily indecomposable Banach spaces, J. A. M. S., 2000, 13: 243–294.

    Article  MATH  MathSciNet  Google Scholar 

  15. Dowson, H. R., Spectral Theory of Linear Operators, New York: JINC, 1978.

    MATH  Google Scholar 

  16. Barnes, B., Muphy, G., Smyth, M. et al., Riesz and Fredholm Theory in Banach Algebras, London: DVK, 1982.

    Google Scholar 

  17. Zhong, H. J., Tsirelson’s space and West decomposition of Riesz operators on it, Science in China, Ser. A, 1996, 39(5): 491–500.

    MATH  Google Scholar 

  18. Kato, T., Perturbation Theory for Linear Operators, New York: Springer-Verlag, 1984.

    MATH  Google Scholar 

  19. Aiena, P., Essentially incomparable Banach spaces and Fredholm theory, Proc. R. Ir. Acad., 1993, 93A(1): 49–59.

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  21. Rudin, W., Functional Analysis, New York: McGraw-Hill, 1991.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhong Huaijie.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhong, H., Chen, D. & Chen, J. Some G-M-type Banach spaces and K-groups of operator algebras on them. Sci. China Ser. A-Math. 47, 372–392 (2004). https://doi.org/10.1360/02ys0372

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/02ys0372

Keywords

Navigation