Stability theorems for linear combinations of idempotents
JJ Koliha, V Rakocevic
INTEGRAL EQUATIONS AND OPERATOR THEORY | SPRINGER BASEL AG | Published : 2007
We prove a stability theorem for the nullity of a linear combination c 1 P 1 + c 2 P 2 of two idempotent operators P 1, P 2 on a Banach space provided c 1, c 2 and c 1 + c 2 are nonzero. We then show that for c 1 P 1 + c 2 P 2 the property of being upper semi-Fredholm, lower semi-Fredholm and Fredholm, respectively, is independent of the choice of c 1, c 2, and that the nullity, defect and index of c 1 P 1 + c 2 P 2 are stable. © 2007 Birkhäuser Verlag Basel/Switzerland.