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Sur les isométries partielles maximales essentielles

Haïkel Skhiri (1998)

Studia Mathematica

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 ....

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