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On spectral properties of linear combinations of idempotents

Tom 180 / 2007

Hong-Ke Du, Chun-Yan Deng, Mostafa Mbekhta, Vladimír Müller 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
  • Vladimír MüllerMathematical Institute
    Czech Academy of Sciences
    Žitná 25
    115 67 Praha 1, Czech Republic
    e-mail

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