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The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces

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Author(s): George Chailos

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 02;
Issue: 02;
Start page: 124;
Date: 2012;
Original page

Keywords: Index | Invariant Subspaces | Bounded below Operators | Banach Spaces

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 .
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