Research ArticleOpen AccessGoogle Scholar indexed
The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces
Department of Computer Science, University of Nicosia, Nicosia, Cyprus
- 1 Department of Computer Science, University of Nicosia, Nicosia, Cyprus
Advances in Pure Mathematics·Volume 02 (2012)·Pages 124–127·Published 22 March 2012·DOI10.4236/apm.2012.22018
Copy link · social · email
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 .
KeywordsIndexInvariant SubspacesBounded below OperatorsBanach Spaces
- G. Chailos, “On Reproducing Kernels and Invariant Subspaces of the Bergman Shift,” Journal of Operator Theory, Vol. 51, No. 1, 2004, pp. 181-200.
- G. Chailos, “Algebraic Properties of the Index of Invariant Subspaces of Operators on Banach Spaces,” Bulletin of the Irish Mathematical Society, Vol. 61, 2008, pp. 9- 13.
- J. B. Conway, “A Course in Functionl Analysis,” 2nd Edition, Springer-Verlag, New York, 1990.
- H. Hedenmalm, B. Korenblum and K. Zhu, “Theory of Bergman Spaces,” Springer-Verlag, New York, 2000. doi:10.1007/978-1-4612-0497-8
- T. Hungerford, “Algebra,” Springer-Verlag, New York, 1996.
- S. Richter, “Invariant Subspaces in Banach Spaces of Analytic Functions,” Transactions of the American Mathematical Society, Vol. 304, No. 2, 1987, pp. 585-616. doi:10.1090/S0002-9947-1987-0911086-8