On majorization and range inclusion of operators on Hilbert C*-modules

摘要

It is proved that for adjointable operators A and B between Hilbert C*-modules, certain majorization conditions are always equivalent without any assumptions on (R(A*))over bar, where A* denotes the adjoint operator of A and (R(A*))over bar is the norm closure of the range of A*. In the case that (R(A*))over bar is not orthogonally complemented, it is proved that there always exists an adjointable operator B whose range is contained in that of A, whereas the associated equation AX = B for adjointable operators is unsolvable.