The Daugavetian Index of a Banach Space
نویسنده
چکیده
Given an infinite-dimensional Banach space X, we introduce the daugavetian index of X , daug (X), as the greatest constant m > 0 such that kId+ Tk > 1 +mkTk for all T ∈ K(X). We givetwo characterizations of this index and we estimate it in some examples. We show that the daugavetian index of a c0-, l1or l∞-sum of Banach spaces is the infimum index of the summands. Finally, we calculate the daugavetian index of some vector-valued function spaces: daug ¡ C(K,X) ¢ ¡ resp. daug ¡ L1(μ,X) ¢ , daug ¡ L∞(μ,X) ¢¢ is the maximum of daug (X) and daug (C(K)) resp. daug (L1(μ)), daug (L∞(μ)).
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