Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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BOUNDARIES FOR AN ALGEBRA OF BOUNDED HOLOMORPHIC FUNCTIONS

  • Moraes, L.A. (Instituto de Matematica Universidade Federal do Rio de Janeiro) ;
  • Grados, L.-Romero (Universidade Estadual de Ponta Grossa)
  • Published : 2004.01.01
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Abstract

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.

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References

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  1. Boundaries for algebras of analytic functions on function module Banach spaces vol.287, pp.7, 2014, https://doi.org/10.1002/mana.201300090
  2. Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces vol.323, pp.2, 2006, https://doi.org/10.1016/j.jmaa.2005.11.028