We consider the best approximation by projections in Banach spaces under certain suitable conditions. Furthermore, applications are discussed for multiplier operators and convolution type operators associated with strongly continuous families of bounded linear operators as well as for homogeneous Banach spaces which include the classical function spaces, as particular cases.
"THE BEST APPROXIMATION BY PROJECTIONS IN BANACH SPACES." Taiwanese J. Math. 5 (2) 375 - 386, 2001. https://doi.org/10.11650/twjm/1500407344