Denseness of Numerical Radius Attaining Holomorphic Functions
نویسندگان
چکیده
LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space of all bounded continuous functions from BX to Y with sup norm ‖f‖ sup {‖f x ‖ : x ∈ BX}. We are interested in the following two subspaces of Cb BX : Y :
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