| A Note on Linearly Isometric Extension for 1-Lipschitz and Anti-1-Lipschitz Mappings between Unit Spheres of $AL_P(\mu,H)$ Spaces |
| Received:March 16, 2011 Revised:August 13, 2011 |
| Key Words:
isometric extension strictly convex Bochner integral.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11271248) and Specific Academic Discipline Project of Shanghai Municipal Education Commission (Grant No.11xk11). |
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| Abstract: |
| In this paper, we show that if $V_0$ is a 1-Lipschitz mapping between unit spheres of $L_P(\mu,H)$ and $L_P(\nu,H)(p>2,~H$ is a Hilbert space), and $-V_0(S(L_p(\mu,H)))\subset V_0(S(L_p(\mu,H)))$, then $V_0$ can be extended to a linear isometry defined on the whole space. If $1 |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.01.013 |
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