It was shown by Fillmore in [1] that linear transformations ?A? and ?T? on a Banach space, with ?A? bounded. If Lat(?A?)?Lat?(T)? under what conditions and ?T? commutes with ?A?, then ?T? is a polynominal in ?A?.

• Fillmore在[1]中得到一个定理:设A；T是Banach空间X上的线性变换；A有界；若Lat(A) Lat(T)且AT=TA；则T是A的多项式.