# STABLE MANIFOLDS FOR NON-AUTONOMOUS EQUATIONS WITH NON-UNIFORM POLYNOMIAL DICHOTOMIES

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Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a...

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Let $A$ be a Banach algebra and let $p$ and $q$ be two positive integers. We show that if $A$ has a left bounded sequential approximate identity $(e_n)_{n\ge1}$ such that ${\rm lim}\,{\rm inf}_{n\to+\infty}\|e^p_n-e^{p+q}_n\| < ({p \over...