ISOMETRIC EMBEDDING OF l1 INTO LIPSCHITZ-FREE SPACES AND l(infinity) INTO THEIR DUALS

Abstrakt

We show that the dual of every infinite-dimensional Lipschitzfree Banach space contains an isometric copy of l(infinity) and that it is often the case that a Lipschitz-free Banach space contains a 1-complemented subspace isometric to l(1). Even though we do not know whether the latter is true for every infinite-dimensional Lipschitz-free Banach space, we show that the space is never rotund.

In the last section we survey the relations between isometric embeddability of l(infinity) into X* and containment of a good copy of l(1) in X for a general Banach space X.

Klíčová slova

• Lipschitz-free spaces
• isometric embedding of l(1)
• isometric embedding of l(infinity)