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Sur les isométries partielles maximales essentielles

100%

Skhiri H.

Studia Mathematica

1998

tom 128

nr 2

135-144

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.

On the perturbation functions and similarity orbits

100%

Skhiri H.

Studia Mathematica

2008

tom 188

nr 1

57-66

We show that the essential spectral radius $ϱ_{e}(T)$ of T ∈ B(H) can be calculated by the formula $ϱ_{e}(T)$ = inf{$ℱ_{♯·♯}(XTX^{-1})$: X an invertible operator}, where $ℱ_{♯·♯}(T)$ is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if $𝒢_{♯·♯}(T)$ is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then $dist(0,σ_{e}(T))$ = sup{$𝒢_{♯·♯}(XTX^{-1})$: X an invertible operator}.

Ograniczanie wyników

2 Studia Mathematica

2 Skhiri H.

1 2008

1 1998

Wyniki wyszukiwania

Sur les isométries partielles maximales essentielles

On the perturbation functions and similarity orbits