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On Hereditarily Indecomposable Banach Spaces

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Abstract

This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi–dual can never have such a one; consequently, every non–separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.

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Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen 361005, P. R. China

    Li Xin Cheng

  2. The Institute of Mathematical Sciences, The Chinese University of Hang Kong, Hang Kong

    Li Xin Cheng

  3. Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China

    Huai Jie Zhong

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  1. Li Xin Cheng
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  2. Huai Jie Zhong
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Correspondence to Li Xin Cheng.

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Research supported by NSFC (Grant No. 10471114 and No. 10471025)

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Cheng, L.X., Zhong, H.J. On Hereditarily Indecomposable Banach Spaces. Acta Math Sinica 22, 751–756 (2006). https://doi.org/10.1007/s10114-005-0614-5

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