We study a Cauchy problem of class nonconvex second-order integro-differential inclusions and boundary value associated to semilinear evolution inclusion defined by nonlocal conditions in non-separable Banach spaces. The existence mild solutions is established under Filippov type assumptions.

Theorem. For X= C(K) the following four statements are equivalent. (i) For every two Banach spaces ZD Y with dim(Z/ Y) = 1 and every operator T from Y into X with a separable range there is an extension T of T from Z into X with \\t\\=\\T\\. •J J 11 11 11 M (ii) For every two Banach spaces ZZ)Y with dim Y =2, dim Z = 3 and every operator T from Y into X there is an extension f of T from Z into ...

A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 ...

We prove that if a non-atomic separable Banach lattice in a weak Hilbert space, then it is lattice isomorphic to L2(0, 1). Introduction This note is to be considered as an addendum to [3], where an extensive study of Banach lattices, which are weak Hilbert spaces, was made. We prove that if a non-atomic separable Banach lattice is a weak Hilbert space then it is lattice isomorphic to L2(0, 1). ...