Affiliation:
1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China
Abstract
Let [Formula: see text] be a linear dynamical system, where [Formula: see text] is a separable Banach space and [Formula: see text] is a bounded linear operator. We show that if [Formula: see text] is invertible, then [Formula: see text] is weakly sensitive compact if and only if [Formula: see text] is thickly weakly sensitive compact; and that there exists a system [Formula: see text] such that: (1) [Formula: see text] is cofinitely weakly sensitive compact; (2) [Formula: see text] and [Formula: see text] are weakly sensitive compact; and (3) [Formula: see text] and [Formula: see text] are not syndetically weakly sensitive compact. We also show that if [Formula: see text] is weakly sensitive compact, where [Formula: see text] is a complex Banach space, then the spectrum of [Formula: see text] meets the unit circle.
Funder
NNSF of China
the Natural Science Foundation of Sichuan Province
Publisher
World Scientific Pub Co Pte Ltd