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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On spectral properties of linear combinations of idempotents

### Tom 180 / 2007

Studia Mathematica 180 (2007), 211-217 MSC: Primary 47B99; Secondary 47A56, 15A99. DOI: 10.4064/sm180-3-2

#### Streszczenie

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.

#### Autorzy

• Hong-Ke DuCollege of Mathematics
and Information Science
Shaanxi Normal University
Xi'an 710062, P.R. China
e-mail
• Chun-Yan DengCollege of Mathematics and Information Science
Shaanxi Normal University
Xi'an 710062, P.R. China
e-mail
• Mostafa MbekhtaUniversité Lille 1, UFR Mathématique
59655 Villeneuve d'Ascq, France
e-mail