Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables

Skihri, Haïkel

Skihri, Haïkel

Studia Mathematica, Tome 133 (1999), p. 229-253 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim of this paper is to study the α-semi-Fredholm operators in a nonseparable Hilbert space H for all cardinals α with $ℵ_{0} \leq α \leq d i m H$ . In the first part, we find the relation between $γ_{α} (T)$ and $c (π_{α} (T))$ for all $ℵ_{0}$ -regular cardinals α, where $γ_{α}$ is the reduced minimum modulus of weight α, c is the reduced minimum modulus (in a C*-algebra) and $π_{α}$ is the canonical surjection from B(H) onto $C_{α} (H) = B (H) / K_{α} (H)$ . We study the continuity points of the maps $c_{α} : T \to c (π_{α} (T))$ and $γ_{α} : T \to γ_{α} (T)$ . In the second part, we prove some approximation results for semi-Fredholm operators. We show that all connected components of semi-Fredholm operators of at most countable index have the same topological boundary. We show that this is not true for indices strictly greater than $ℵ_{0}$ .

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216669

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     title = {Les op\'erateurs semi-Fredholm sur des espaces de Hilbert non s\'eparables},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {229-253},
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Skihri, Haïkel. Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables. Studia Mathematica, Tome 133 (1999) pp. 229-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i3p229bwm/

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