The problem of isometric extension on the unit sphere of the space \(l\cap l^p(H)\) for \(0 < p < 1\). (English) Zbl 1330.46006
Summary: In this paper, we study the problem of isometric extension on the unit sphere of the space \(l\cap l^p(H)\) for \(0<p<1\). We obtain that an isometric mapping of the unit sphere \(S(l\cap l^p(H))\) onto itself can be extended to an isometry on the whole space \(l\cap l^p(H)\).
MSC:
| 46A16 | Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) |
| 46B04 | Isometric theory of Banach spaces |
| 46E40 | Spaces of vector- and operator-valued functions |
