Spectral characterization of asymptotic expansivity

Determine whether a subset of the spectrum of a bounded linear operator characterizes asymptotic expansivity.

Background

The paper shows that asymptotic expansivity cannot be characterized using the point spectrum, approximate point spectrum, or entire spectrum alone: two forward-shift examples have the same relevant spectral data but differ in asymptotic expansivity. The authors therefore ask whether some suitable subset of the spectrum can provide a complete characterization.

References

Open Question 1: Is there any subset of the spectrum which characterizes asymptotic expansivity?

— Asymptotic Expansive and Hyperbolic Linear Operators  (2610.01196 - Bag et al., 1 Oct 2026) in Section "Open Questions", Open Question 1; see also Example 3.7 (labeled "nochar")