Sentence:  If * * f are the projections associated with the <WSD>primary</WSD> decomposition of T , then each * * f is 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:  of first rank or importance or value; direct and immediate rather than secondary