Power growth of mean-L-stable operators on Banach spaces

What the math gives to ML

The paper supplies a constructive stability diagnostic for iterated linear dynamics: instead of requiring every power of an operator to remain bounded, it controls the density of time indices at which orbit norms exceed a threshold. The key transferable asset is robustness to rare transient spikes, which ordinary spectral-radius checks can miss in non-normal recurrent or state-space operators. A practical adaptation is to monitor and penalize empirical high-norm time density in recurrent states, while using the paper's power-growth bounds as a safety target rather than assuming strict contraction.