$AL_P(\mu,H)$空间中单位球面间1-Lipschitz和反1-Lipschitz映射的线性等距延拓的一个注记

A Note on Linearly Isometric Extension for 1-Lipschitz and Anti-1-Lipschitz Mappings between Unit Spheres of $AL_P(\mu,H)$ Spaces

中文关键词:  1-Lipschitz映射  反1-Lipschitz映射  Bochner积分  Hilbert空间  严格凸  线性等距延拓.

英文关键词:isometric extension  strictly convex  Bochner integral.

中文摘要:

      作者证明了：如果$p>2,V_0$是$S(L_p(\mu,H))$到$S(L_p(\nu,H))$内的1-Lipshitz 映射，且$-V_0(S(L_p(\mu,H)))\subset V_0(S(L_p(\mu,H))),$ 则$V_0$ 可(实)线性等距延拓到整个$L_p(\mu,H)$；如果$1

英文摘要:

      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