Sentence:  If * * f are the projections associated with the primary decomposition of T , then each * * f is a polynomial in T , and accordingly if a <WSD>linear</WSD> operator U commutes with T then U commutes with each of the * * f i.e. , each subspace * * f is invariant under U . 
Meaning of the word marked with <WSD> tags:  an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)