首页|A generalization of Banach's lemma and its applications to perturbations of bounded linear operators
A generalization of Banach's lemma and its applications to perturbations of bounded linear operators
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Let X be a Banach space and let P:X →X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)-1 as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.
NETL
NSTL
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