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 subspace * * f is <WSD>invariant</WSD> under U . 
Meaning of the word marked with <WSD> tags:  unaffected by a designated operation or transformation