Some results concerning proximinality and co-proximinality

A new method for approximation of closed convex subsets of B(H)

“…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]).…”

Complemented subspaces in the normed spaces

“…al [8][9][10][11][12]. Also there are some results on coapproximation in [2][3][4][5]. In this context, we shall obtain some results on orthogonality and coproximinality subspaces of normed space, and obtain properties on normed spaces that are similar to orthogonality in Hilbert spaces.…”

Proximinality and co-proximinality in metric linear spaces

“…This study was further taken up by many researchers in normed linear spaces and Hilbert spaces (see e.g. [3], [4], [9]). But only a few have taken up this study in more general abstract spaces.…”