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On interpolation by analytic maps in infinite dimensions

  • J. Globevnik (a1)

Let A be the complex Banach algebra of all bounded continuous complex-valued functions on the closed unit ball of a complex Banach space X, analytic on the open unit ball, with sup norm. For a class of spaces X which contains all infinite dimensional complex reflexive spaces we prove the existence of non-compact peak interpolation sets for A. We prove some related interpolation theorems for vector-valued functions and present some applications to the ranges of analytic maps between Banach spaces. We also show that in general peak interpolation sets for A do not exist.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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