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Let X and Y be infinite-dimensional complex Banach spaces, and
(Y)) be the algebra of all bounded linear operators on X (resp. on Y). For an operator T ∈
(X) and a vector x ∈ X, let σT(x) denote the local spectrum of T at x. For two nonzero vectors x0 ∈X and y0 ∈ Y, we show that a map ϕ from