Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables
Studia Mathematica, Tome 136 (1999) no. 3, pp. 229-253
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The aim of this paper is to study the α-semi-Fredholm operators in a nonseparable Hilbert space H for all cardinals α with $ℵ_0 ≤ α ≤ dim H$. 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 $c_α : T → c(π_α(T))$ and $γ_α : T → γ_α(T)$. 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 $ℵ_0$.
@article{10_4064_sm_136_3_229_253,
author = {Ha{\"\i}kel Skihri},
title = {Les op\'erateurs {semi-Fredholm} sur des espaces de {Hilbert} non s\'eparables},
journal = {Studia Mathematica},
pages = {229--253},
publisher = {mathdoc},
volume = {136},
number = {3},
year = {1999},
doi = {10.4064/sm-136-3-229-253},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-136-3-229-253/}
}
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%0 Journal Article %A Haïkel Skihri %T Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables %J Studia Mathematica %D 1999 %P 229-253 %V 136 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-136-3-229-253/ %R 10.4064/sm-136-3-229-253 %G fr %F 10_4064_sm_136_3_229_253
Haïkel Skihri. Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables. Studia Mathematica, Tome 136 (1999) no. 3, pp. 229-253. doi: 10.4064/sm-136-3-229-253
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