A note on extension of isometric embedding from a Banach space E into the universal space l(infinity)(Gamma)

作者：Liu Rui^*

来源：Journal of Mathematical Analysis and Applications, 2010, 363(1): 220-224.

DOI：10.1016/j.jmaa.2009.08.033

• Isometric embedding
• Unit sphere
• Universal space

In this paper we shall present a short proof on the extension problem of isometric embedding between unit spheres of a Banach space E and the universal space l(infinity)(Gamma). We prove that, under some condition, every isometric embedding from S(E) into S(l(infinity)(Gamma)) can be positive-homogeneously isometrically extended to the whole space. Since every Banach space E is isometric to a subspace of l(infinity)(S(E*)), isometric extension problems on a class of atomic AM-spaces is solved.

• 出版日期2010-3-1
• 单位南开大学