Composition, numerical range and Aron-Berner extension

• Autores: Yun-Sung Choi, Domingo García Rodríguez, Sung Guen Kim, Manuel Maestre Vera
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 103, Nº 1, 2008, págs. 97-110
• Idioma: inglés
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• Resumen

  • Given an entire mapping f ¡ô Hb(X,X) of bounded type from a Banach space X into X, we denote by f theAron-Berner extension of f to the bidual X.. of X.We show that g . f = g . f for all f, g ¡ô Hb(X,X) if X is symmetrically regular.We also give a counterexample on l1 such that the equality does not hold.We prove that the closure of the numerical range of f is the same as that of f..