Composition, numerical range and Aron-Berner extension

Authors

  • Yun Sung Choi
  • Domingo García
  • Sung Guen Kim
  • Manuel Maestre

DOI:

https://doi.org/10.7146/math.scand.a-15071

Abstract

Given an entire mapping fHb(X,X) of bounded type from a Banach space X into X, we denote by ¯f the Aron-Berner extension of f to the bidual X of X. We show that ¯gf=¯g¯f for all f,gHb(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 ˉf.

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Published

2008-09-01

How to Cite

Choi, Y. S., García, D., Kim, S. G., & Maestre, M. (2008). Composition, numerical range and Aron-Berner extension. MATHEMATICA SCANDINAVICA, 103(1), 97–110. https://doi.org/10.7146/math.scand.a-15071

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Articles