On a fixed-point theorem of Banach type
Jochen Reinermann (1970)
Annales Polonici Mathematici
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Displaying similar documents to “Extremal properties of the set of vector-valued Banach limits”
On a fixed-point theorem of Banach type
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For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...
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