Geodesic
Sur les isométries partielles maximales essentielles
Studia Mathematica, Tome 128 (1998) no. 2, pp. 135-144

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We study the problem of approximation by the sets S + K(H), $S_e$, V + K(H) and $V_e$ where H is a separable complex Hilbert space, K(H) is the ideal of compact operators, $S = {L ∈ B(H) : L*L = I}$ is the set of isometries, V = S ∪ S* is the set of maximal partial isometries, $S_e = {L ∈ B(H): π(L*)π( L) = π(I)}$ and $V_e = S_e ∪ S_e*$ 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 $V_e = V + K(H)$. We also show that S + K(H) is both closed and open in $S_e$. Finally, we prove that $V_e$, S + K(H) and $S_e$ coincide with their boundaries $∂(V_e)$, ∂(S + K(H)) and $∂(S_e)$ respectively.
DOI : 10.4064/sm-128-2-135-144

Haïkel Skhiri 1

1 
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Haïkel Skhiri. Sur les isométries partielles maximales essentielles. Studia Mathematica, Tome 128 (1998) no. 2, pp. 135-144. doi: 10.4064/sm-128-2-135-144

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