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Boundaries for an algebra of bounded holomorphic functions

L. A. Moraes|L. Romero Grados
대한수학회 (The Korean Mathematical Society)|2004.01|대한수학회지 (Journal of the KMS)|제41권 제1호|pp. 231-242

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Abstract

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.

참고문헌 (7)

  1. "Boundaries foralgebras of analytic functions on innite dimensional Banach spaces", pp.1522~ (1992)
  2. "There is no bilinear Bishop-Phelps theorem", 93, pp.221~228 (1996)
  3. "On interpolation by analytic maps in innite dimensions", 83 (1978)
  4. null, "Boundaries for polydisc algebras in innite dimensions", 85 (1979)
  5. "Symmetric block bases of sequences with large average growth", 69 (1990)
  6. "Boundaries for algebras of holomorphicfunctions", 281, pp.575~586 (2003)
  7. "Norm attaining multilinear forms and polyno-mials on preduals of Lorentz sequence spaces", 127(2), pp.99~111 (1998)

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