DISJOINTNESS OF OPERATOR RANGES IN BANACH SPACES

摘要

LetXbe a Banach space. A linear subspace ofXis called an operator range if it coincides with the range of a bounded linear operator defined on some Banach space. The paper studies disjointness and inclusion properties of various types of operator ranges in a separable infinite dimensional Banach spaceX.One of the main results is the following: LetEbe a non-closed operator range inX.ThenXcontains a non-closed dense operator rangeRwith the propertiesE#x2229;= {0}, andRis decomposable, i.e.R=M+NwhereM,Nare closed and infinite dimensional andM#x2229;N= {0} (Theorem 6.2).