Sur les isométries partielles maximales essentielles
Skhiri, Haïkel
Studia Mathematica, Tome 129 (1998), p. 135-144 / Harvested from The Polish Digital Mathematics Library
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We study the problem of approximation by the sets S + K(H), Se, V + K(H) and Ve 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, Se=L∈B(H):π(L*)π(L)=π(I) and Ve=Se∪Se* 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 Ve=V+K(H). We also show that S + K(H) is both closed and open in Se. Finally, we prove that Ve, S + K(H) and Se coincide with their boundaries ∂(Ve), ∂(S + K(H)) and ∂(Se) respectively.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:216479 
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     title = {Sur les isom\'etries partielles maximales essentielles},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {135-144},
     zbl = {0904.47013},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv128i2p135bwm}
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Skhiri, Haïkel. Sur les isométries partielles maximales essentielles. Studia Mathematica, Tome 129 (1998) pp. 135-144. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv128i2p135bwm/

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