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 linear operator U commutes with T <WSD>then</WSD> U commutes with each of the * * f i.e. , each subspace * * f is invariant under U . 
Meaning of the word marked with <WSD> tags:  in that case or as a consequence