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Range inclusion of operators on non-archimedean Banach space

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Abstract

In this paper, we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields. These theorems provide close relationship among range inclusion, majorization and factorization for bounded linear operators. It is found that these results depend strongly on a continuous extension property, which is always true in the classical archimedean case, but may fail to hold for the nonarchimedean setting. Several counterexamples are given to show that our results are sharp in some sense.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, **an, 250100, China

    PengHui Wang

  2. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Bei**g, 100190, China

    Xu Zhang

  3. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Xu Zhang

Authors
  1. PengHui Wang
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  2. Xu Zhang
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Correspondence to PengHui Wang.

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Wang, P., Zhang, X. Range inclusion of operators on non-archimedean Banach space. Sci. China Math. 53, 3215–3224 (2010). https://doi.org/10.1007/s11425-010-4130-4

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  • DOI: https://doi.org/10.1007/s11425-010-4130-4

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