Quasi-compactness and uniform stabilization on general Banach spaces under $θ$-subordinate perturbations of semigroup generators

We prove that the quasi-compactness of an analytic semigroup is preserved under $θ$-subordinate perturbations of its generator on general Banach spaces, provided the perturbations are compact along trajectories. This allows us to prove the permanence of uniform exponential stability for an analytic