猜测“存在Banach空间X使得K0(B(X))=Z2”的一个注记

张云南, 林丽琼

数学学报 ›› 2011, Vol. 54 ›› Issue (2) : 313-320.

PDF(443 KB)
PDF(443 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (2) : 313-320. DOI: 10.12386/A2011sxxb0032
论文

猜测“存在Banach空间X使得K0(B(X))=Z2”的一个注记

    张云南1, 林丽琼1,2
作者信息 +

A Note on the Guess “There Exists a Banach Space X with K0(B(X)) = Z2

    Yun Nan ZHANG1, Li Qiong LIN1,2
Author information +
文章历史 +

摘要

讨论Banach空间X上算子代数B(X)的K0群,给出K0(B(X))=Z2的2个充分条件.

 

Abstract

This paper discusses the K0-group of the operator algebra B(X) on Banach space X and gives two sufficient conditions for K0(B(X)) = Z2.

 

关键词

Banach空间 / 算子代数 / K0

Key words

Banach spaces / operator algebras / K0-groups

引用本文

导出引用
张云南, 林丽琼. 猜测“存在Banach空间X使得K0(B(X))=Z2”的一个注记. 数学学报, 2011, 54(2): 313-320 https://doi.org/10.12386/A2011sxxb0032
Yun Nan ZHANG, Li Qiong LIN. A Note on the Guess “There Exists a Banach Space X with K0(B(X)) = Z2”. Acta Mathematica Sinica, Chinese Series, 2011, 54(2): 313-320 https://doi.org/10.12386/A2011sxxb0032

参考文献


[1] Elliott G. A., On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra, 1976, 38: 29-44.

[2] Gowers W. T., Maurey B., The unconditional basic sequence problem, J. Amer. Math. Soc., 1993, 6(3): 851-874.

[3] Gowers W. T., Maurey B., Banach spaces with small spaces of operators, Math. Ann., 1997, 307: 543-568.

[4] Lindenstrauss J., The work of Gowers W T. Notices Amer. Math. Soc., 1999, 46(1): 19-20.

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

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

[7] Laustsen N. J., K-Theory for the Banach algebras of operators on James’ quasi-reflexive Banach spaces, K-Theory, 2000, 23: 115-127.

[8] Laustsen N. J., Divisibility in the K0-Group of the algebra of operators on a Banach space, K-Theory, 2001, 22: 241-249.

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

[10] Zhang Y. N., Zhong H. J., Su W. G., On K0 groups of operator algebras on Banach spaces, Science in China, 2006, 49(2): 233-244.

[11] Blackadar B., K-Theory for Operator Algebras, New York: Springer-Verlag, 1986.

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

基金

国家自然科学基金资助项目(10926173);福建省自然科学基金资助项目(2009J05002)

PDF(443 KB)

308

Accesses

0

Citation

Detail

段落导航
相关文章

/