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(Lμ1). Acta Mathematica Sinica, English Series, 22(6), 1721–1724 (2006)].
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