Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (2): 387-394.

• Articles • Previous Articles     Next Articles

On Extension of Isometries Between Unit Spheres in ALp-spaces (1<p<∞)

 GAO Jin-Mei1, TAN Dong-Ni2   

  1. 1.School of Mathematics, Qingdao University, Shandong Qingdao 266071;
    2.School of Mathematics, Tianjin University of Technology, Tianjin 300071
  • Received:2010-11-25 Revised:2011-12-30 Online:2012-04-25 Published:2012-04-25
  • Supported by:

    教育部博士点基金(20060055010)和国家自然科学基金 (41171183)资助

Abstract:

In this paper, we discuss the 1-Lipschitz mappings between the unit spheres in vector valued spaces Lp(Ω, ∑, μ; Lq(X, Aν)) (2≤q<p<∞) and anti-1-Lipschitz mappings between the unit spheres in  vector valued spaces Lp (Ω, ∑, μ; Lq(XAν))(1<p<≤2), and obtain that every such mapping can be extended to be a real linear isometry on the whole space Lp(Ω, ∑, μ; Lq(XA, ν)).

CLC Number: 

  • 46B04
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