Good projections of spaces of vector measures onto subspaces of Bochner integrable functions

Abstract

We show that the complementability of L₁(μ, X)
in cabv(μ, X) implies the complementability of L₁(μ, K(Z,
X)) in
cabv(μ, K(Z, X)),
provided the projection from cabv(μ, X) onto L₁(μ, X) is “good”,
Z* is separable and K(Z, X)
= L(Z, X),. The projection got is also
“good”, so that it allows to construct a projection from the space
L(L₁(μ),
K(Z, X)) onto the
subspace R(L₁(μ), K(Z, X)) of
all representable operators.


Mathematics Subject
Classification (2000): 28B05, 46G10, 46B20, 46B28, 47L05



Quaestiones Mathematicae 25 (2002), 237-245