Boundaries for spaces of holomorphic functions on M-ideals in their biduals Mara­a AcostaRichard AronLuiza Moraes 46J1546B4546G2032A40holomorphic functionboundarypeak pointstrong peak set For a complex Banach space $X$, let $\mathcal{A}_{u}(B_X)$ be the Banach algebra of all complex valued functions defined on $B_{X}$ that are uniformly continuous on $B_{X}$ and holomorphic on the interior of $B_{X}$, and let $\mathcal{A}_{wu}(B_X)$ be the Banach subalgebra consisting of those functions in $\mathcal{A}_{u}(B_X)$ that are uniformly weakly continuous on $B_{X}$. In this paper we study a generalization of the notion of \emph{boundary} for these algebras, originally introduced by Globevnik. In particular, we characterize the boundaries of $\mathcal{A}_{wu}(B_X)$ when the dual of $X$ is separable. We exhibit some natural examples of Banach spaces where this characterization provides concrete criteria for the boundary. We also show that every non-reflexive Banach space $X$ which is an $M$-ideal in its bidual cannot have a minimal closed boundary for $\mathcal{A}_{u}(B_X)$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3807 10.1512/iumj.2009.58.3807 en Indiana Univ. Math. J. 58 (2009) 2575 - 2596 state-of-the-art mathematics http://iumj.org/access/