Any Banach space has an equivalent norm with trivial isometries |
| |
| Authors: | K Jarosz |
| |
| Institution: | (1) Institute of Mathematics, Warsaw University, P.K.i N. IXp., 00-901 Warsaw, Poland;(2) Department of Mathematics, University of California S.B., 93106 Santa Barbara, CA, USA;(3) Present address: Department of Mathematics and Statistics, SIUE, 62026 Edwardsville, IL, USA |
| |
| Abstract: | For any Banach spaceX there is a norm |||·||| onX, equivalent to the original one, such that (X, |||·|||) has only trivial isometries. For any groupG there is a Banach spaceX such that the group of isometries ofX is isomorphic toG × {− 1, 1}. For any countable groupG there is a norm ‖ · ‖
G
onC(0, 1]) equivalent to the original one such that the group of isometries of (C(0, 1]), ‖ · ‖
G
) is isomorphic toG × {−1, + 1}. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
