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

Haïkel Skihri

Studia Mathematica (1999)

  • Volume: 136, Issue: 3, page 229-253
  • ISSN: 0039-3223

Abstract

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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 ≤ 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 → 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 .

How to cite

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Skihri, Haïkel. "Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables." Studia Mathematica 136.3 (1999): 229-253. <http://eudml.org/doc/216669>.

@article{Skihri1999,
author = {Skihri, Haïkel},
journal = {Studia Mathematica},
language = {fre},
number = {3},
pages = {229-253},
title = {Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables},
url = {http://eudml.org/doc/216669},
volume = {136},
year = {1999},
}

TY - JOUR
AU - Skihri, Haïkel
TI - Les opérateurs semi-Fredholm sur des espaces de Hilbert non séparables
JO - Studia Mathematica
PY - 1999
VL - 136
IS - 3
SP - 229
EP - 253
LA - fre
UR - http://eudml.org/doc/216669
ER -

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