On spectral properties of linear combinations of idempotents
Volume 180 / 2007
Studia Mathematica 180 (2007), 211-217 MSC: Primary 47B99; Secondary 47A56, 15A99. DOI: 10.4064/sm180-3-2
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.