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

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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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