The () Property in Banach Spaces
A Banach space is said to have ( D ) property if every bounded linear operator is weakly compact for every Banach space whose dual does not contain an isomorphic copy of . Studying this property in connection with other geometric properties, we show that every Banach space whose dual has ( V ∗ ) property of Pełczyński (and hence every Banach space with ( V ) property) has ( D ) property. We show that the space of real functions, which are integrable with respect to a measure with values in a Banach space , has ( D ) property. We give some other results concerning Banach spaces with ( D ) property.