A note on polynomial operator approximation Academic Article

An example is given of an operator T T contained in a block-diagonal algebra of operators A mathcal {A} , an ideal J A J subset mathcal {A} and an infinite set of polynomials P mathcal {P} for which there is a K J K in J satisfying p ( T + K ) A = p ( T + K ) A / J {left | {p(T + K)}
ight |_{mathcal {A}}} = {left | {p(T + K)}
ight |_{mathcal {A}/J}} for any finite subset of P mathcal {P} but for which there is no K J K in J satisfying p