Weak Sensitive Compactness for Linear Operators.

Let (X , T) be a linear dynamical system, where X is a separable Banach space and T : X → X is a bounded linear operator. We show that if (X , T) is invertible, then (X , T) is weakly sensitive compact if and only if (X , T) is thickly weakly sensitive compact; and that there exists a system (X × Y , T × S) such that: (1) (X × Y , T × S) is cofinitely weakly sensitive compact; (2) (X , T) and (Y , S) are weakly sensitive compact; and (3) (X , T) and (Y , S) are not syndetically weakly sensitive compact. We also show that if (X , T) is weakly sensitive compact, where X is a complex Banach space, then the spectrum of T meets the unit circle. [ABSTRACT FROM AUTHOR]