Sentence:  If * * f are the <WSD>projections</WSD> 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 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:  a prediction made by extrapolating from past observations