Sur le théorème de point fixe de Brunel et le théorème de Choquet-Deny
We study the problem of approximation by the sets S + K(H), , V + K(H) and where H is a separable complex Hilbert space, K(H) is the ideal of compact operators, is the set of isometries, V = S ∪ S* is the set of maximal partial isometries, and where π : B(H) → B(H)/K(H) denotes the canonical projection. We also prove that all the relevant distances are attained. This implies that all these classes are closed and we remark that . We also show that S + K(H) is both closed and open in ....