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In this paper, we characterize the numerical and numerical strong-peak points for A ∞ (B E : E) when E is the complex space l 1 or C(K). We also prove that {(x, x*) ∈ Π(l 1 ): |x*(e n )| = 1 for all n ∈ N} is the numerical Silov boundary for A ∞ (Bl 1 : l 1 ).

Numerical peak points and numerical Šilov boundary for holomorphic functions