Restrictions of an Invertible Chaotic Operator to Its Invariant Subspaces

Author(s)

Kit C. Chan, Bowling Green State UniversityFollow
Gokul R. Kadel

Document Type

Article

Abstract

Let M be a closed subspace of a separable, infinite dimensional Hilbert space H with dim(H/M)=∞. We show that a bounded linear operator A:M→M has an invertible chaotic extension T:H→H if and only if A is bounded below. Motivated by our result, we further show that A:M→M has a chaotic Fredholm extension T:H→H if and only if A is left semi-Fredholm.

Repository Citation

Chan, Kit C. and Kadel, Gokul R., "Restrictions of an Invertible Chaotic Operator to Its Invariant Subspaces" (2014). Mathematics and Statistics Faculty Publications. 33.
https://scholarworks.bgsu.edu/math_stat_pub/33

Publication Date

2014

Publication Title

Journal of Mathematical Analysis and Applications

Publisher

Elsevier

DOI

https://doi.org/10.1016/j.jmaa.2013.07.072

Volume

409

Issue

2

Start Page No.

996

End Page No.

1004