THE FIXED POINT PROPERTY AND THE OPIAL CONDITION ON TREE-LIKE BANACH SPACES

We introduce some new tree-like Banach spaces, belonging to the class of separable Banach spaces not containing L-1 with non-separable dual, each one of which satisfies the following: (1) the space has the fixed point property and (2) the space does not satisfy the Opial condition. In addition, one of these spaces contains subspaces isomorphic to c(0), whose Banach-Mazur distance from c(0) becomes arbitrarily large.