Answer to Question #8297 in Functional Analysis for Muhammad Imran

Question #8297
Let X be complex Banach space , T Є B(X,X) and p a polynomial .Show that the equation p(T)x = y has a unique solution x for every y ЄX if and only if p(λ)≠0 , for all λ Є σ(T)
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Expert's answer
2012-04-12T07:27:46-0400
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