Sentence:  If * * f are the projections associated with the primary decomposition of T , then each * * f <WSD>is</WSD> a polynomial in T , and accordingly if a linear 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:  be identical to; be someone or something