Abstract :
Two methods which can be used to show that, on a Banach space X, every bounded linear operator has a best compact approximation, namely the basic inequality method and the method of M-ideals, are shown to be basically equivalent. Thus, the paper responds to a question posed by S. Axler, I. D. Berg, N. Jewell, and A. Shields (1979, Ann. of Math.109, 601-612; 1980, Trans. Amer. Math. Soc.261, 159-167).
