The Index of Invariant Subspaces of Bounded below Operators on 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 .
Share and Cite:
G. Chailos, "The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces,"
Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 124-127. doi:
10.4236/apm.2012.22018.
Conflicts of Interest
The authors declare no conflicts of interest.
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