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A remark on extension of into isometries

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Abstract

In this paper, we prove that an into isometry form S(l ∞(n) ) to S(E), which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.: The isometric extension of an into mapping from the unit sphere S(l ∞(2) ) to S(L 1 μ ). Acta Mathematica Sinica, English Series, 22(6), 1721–1724 (2006)].

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Authors and Affiliations

  1. School of Mathematics, Nankai University, Tianjin, 300071, P. R. China

    Rui Dong Wang

  2. Department of Mathematics, Tianjin University of Technology, Tianjin, 300191, P. R. China

    Rui Dong Wang

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  1. Rui Dong Wang
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Correspondence to Rui Dong Wang.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10871101) and the Doctoral Programe Foundation of Institution of Higher Education (Grant No. 20060055010)

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Wang, R.D. A remark on extension of into isometries. Acta. Math. Sin.-English Ser. 26, 203–208 (2010). https://doi.org/10.1007/s10114-010-6656-3

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  • DOI: https://doi.org/10.1007/s10114-010-6656-3

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