Geodesic
On spectral properties of linear combinations of idempotents
Hong-Ke Du1 ; Chun-Yan Deng1 ; Mostafa Mbekhta2 ; Vladimír Müller3
1 College of Mathematics and Information Science Shaanxi Normal University Xi'an 710062, P.R. China
2 Université Lille 1, UFR Mathématique 59655 Villeneuve d'Ascq, France
3 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic
Studia Mathematica, Tome 180 (2007) no. 3, pp. 211-217

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $P,Q$ be two linear idempotents on a Banach space. We show that the closedness of the range and complementarity of the kernel (range) of linear combinations of $P$ and $Q$ are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties of linear combinations do not depend on their coefficients.
DOI : 10.4064/sm180-3-2
Keywords: linear idempotents banach space closedness range complementarity kernel range linear combinations independent choice coefficients generalizes known results shows many spectral properties linear combinations depend their coefficients

Hong-Ke Du 1 ; Chun-Yan Deng 1 ; Mostafa Mbekhta 2 ; Vladimír Müller 3

1 College of Mathematics and Information Science Shaanxi Normal University Xi'an 710062, P.R. China
2 Université Lille 1, UFR Mathématique 59655 Villeneuve d'Ascq, France
3 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic 
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Hong-Ke Du; Chun-Yan Deng; Mostafa Mbekhta; Vladimír Müller. On spectral properties of
 linear combinations of idempotents. Studia Mathematica, Tome 180 (2007) no. 3, pp. 211-217. doi: 10.4064/sm180-3-2

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