A display of a topological group G on a Banach space X is a topological
isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm
||.|| on X, where the latter group is equipped with the strong operator
topology.
Displays of Polish groups on separable real spaces are studied. It is proved
that any closed subgroup of the infinite symmetric group S_\infty containing a
non-trivial central involution admits a display on any of the classical spaces
c0, C([0,1]), lp and Lp for 1 <=p <\infty. Also, for any Polsih group G, there
exists a separable space X on which {-1,1} x G has a display.Comment: 27 page
