Share This Article:

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

Abstract Full-Text HTML Download Download as PDF (Size:77KB) PP. 124-127
DOI: 10.4236/apm.2012.22018    5,615 Downloads   10,506 Views  
Author(s)    Leave a comment

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 .

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

[1] G. Chailos, “On Reproducing Kernels and Invariant Subspaces of the Bergman Shift,” Journal of Operator Theory, Vol. 51, No. 1, 2004, pp. 181-200.
[2] 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.
[3] J. B. Conway, “A Course in Functionl Analysis,” 2nd Edition, Springer-Verlag, New York, 1990.
[4] H. Hedenmalm, B. Korenblum and K. Zhu, “Theory of Bergman Spaces,” Springer-Verlag, New York, 2000. doi:10.1007/978-1-4612-0497-8
[5] T. Hungerford, “Algebra,” Springer-Verlag, New York, 1996.
[6] 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

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.