A canonical trace class approximant Academic Article

Let H H be a finite-dimensional Hilbert space, B ( H ) Bleft ( H
ight ) the space of bounded linear operators on H H , and C C a convex subset of B ( H ) Bleft ( H
ight ) . If A A is a fixed operator in B ( H ) Bleft ( H
ight ) , then A A has a unique best approximant from C C in the C P {C_P} norm for 1 > p > 1 > p > infty . However, in the C 1 {C_1} (trace) norm, A A may have many best approximants from C C . In this paper, it is shown that the best C p {C_p} approximants to A A