Composition, numerical range and Aron-Berner extension - Choi, Yun Sung; García, Domingo; Kim, Sung Guen; Maestre, Manuel (Mathematica Scandinavica, 2008)
Given an entire mapping fH_b(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 g° f = g° f for all f, gH_b(X,X) if X is symmetrically regular. We also give a counterexample on l_1 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.