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 then U commutes with each of the * * f i.e. , each <WSD>subspace</WSD> * * f is invariant under U . 
Meaning of the word marked with <WSD> tags:  a space that is contained within another space