TITLE:
The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces
AUTHORS:
George Chailos
KEYWORDS:
Index; Invariant Subspaces; Bounded below Operators; Banach Spaces
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.2,
March
22,
2012
ABSTRACT: For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .