Numerical peak points and numerical Šilov boundary for holomorphic functions

Kim, Sung Guen

doi:10.1090/S0002-9939-08-09402-1

Numerical peak points and numerical Šilov boundary for holomorphic functions
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Proc. Amer. Math. Soc. 136 (2008), 4339-4347 Request permission

Abstract:

In this paper, we characterize the numerical and numerical strong-peak points for ${\mathcal A}_{\infty }(B_{E}:E)$ when $E$ is the complex space $l_1$ or $C(K)$. We also prove that $\{(x, x^*)\in \Pi (l_1):|x^*(e_n)|=1~\mbox {for all}~n\in \mathbb {N} \}$ is the numerical Šilov boundary for ${\mathcal A}_{\infty }(B_{l_1}:l_1).$

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