“…The theory of best approximation by elements of convex sets in normed linear spaces, have been studied by many investigators. Some results on existence and uniqueness of best approximation and coapproximation in general Banach spaces can be found in [1,4,6,8,11,14,17,19]. The Noncommutative approximation and, in particular, approximation in the space of Hilbert operator has a long history (see for example, [2,9,10,12,20]).…”