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

DOI: 10.4236/apm.2012.22018   PDF   HTML     5,831 Downloads   10,749 Views  

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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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.

References

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