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Boundaries for an algebra of bounded holomorphic functions
L. A. Moraes,L. Romero Grados 대한수학회 2004 대한수학회지 Vol.41 No.1
Let Ab(BE) be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball BE of a complex Banach space E, and holomorphic in the interior of BE, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for Ab(BE) in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for Ab(BE) and give some examples of boundaries.
BOUNDARIES FOR AN ALGEBRA OF BOUNDED HOLOMORPHIC FUNCTIONS
Moraes, L.A.,Grados, L.-Romero Korean Mathematical Society 2004 대한수학회지 Vol.41 No.1
Let $A_b(B_E)$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $B_E$ of a complex Banach space E, and holomorphic in the interior of $B_E$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $A_b(B_E)$ in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for $A_b(B_E)$ and give some examples of boundaries.