Distance and best approximations in operator norm and trace class norm

Abstract

We study the best approximation and distance problems in the operator space $\B(\HS)$ and in the space of trace class operators $\LS^1(\B(\HS))$. Formulations of distances are obtained in both cases. The case of finite-dimensional $C^{\ast }$-algebras is also considered. The computational advantage of the results is illustrated through examples.

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