  We consider *-linear maps into a commutative C*-algebra C (X) of continuous
functions on a locally compact Hausdorff space X with certain specified
properties and prove two results: (1) an extension result for a class of
*-linear maps Y --> C (X) which may be called of locally compact type (locally
finite) with respect to an inclusion Y < X of normed vector spaces, and (2) a
minimal decomposition for certain *-linear maps into C (X) (absolutely
continuous) as a difference of two positive maps.
