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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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(5) J. Globevnik The Rudin-Carleson theorem for vector-valued functions. Proc. Amer. Math. Soc. 53 (1975), 250252.

(6) J. Globevnik Analytic functions whose range is dense in a ball. J. Funct. Anal. 22 (1976), 3238.

(7) J. Globevnik The range of vector-valued analytic functions. Arkiv för Mat. 14 (1976), 113118. The range of vector-valued analytic functions: II. Arkiv för Mat. 14 (1976), 297298.

(15) J. Lindenstrauss On operators which attain their norm. Israel J. Math. 1 (1963), 139148.

(16) A. Pełczyński Some linear topological properties of separable function algebras. Proc. Amer. Math. Soc. 18 (1967), 652661.

(23) E. Thorp and R. Whitley The strong maximum modulus theorem for analytic functions into a Banach space. Proc. Amer. Math. Soc. 18 (1967), 640646.

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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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