Sur les isométries partielles maximales essentielles

• Autorzy: Haïkel Skhiri
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A58: Operator approximation theory
• 47A53: (Semi-) Fredholm operators; index theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 2
• Strony: 135-144

Daty

wydano

1998

otrzymano

1996-10-15

poprawiono

1997-09-12

Twórcy

autor

Haïkel Skhiri

• URA au CNRS et UFR de Mathématiques, Bât. M2, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France,

Bibliografia

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