On the <i>MT</i>*- and λ-Conjugates of Spaces

Marston Morse and William Transue (9, 10), motivated by their theory of bilinear functions, introduced and studied vector function spaces called MT -spaces for which each element of the dual is represented by an integral with respect to a suitable ( C ) measure. In this paper the definition of real MT -spaces is generalized to give spaces, called MT *-spaces, for which part but not all of the dual is of integral type and this part is called the MT *- conjugate of the space.