Stability Theorems for Linear Combinations of Idempotents
Tóm tắt
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.