Banach envelopes of p-banach lattices, 0 < p < 1, and cesàro spaces


In this note we characterize Banach envelopes of p-Banach lattices, 0 < p < 1, such that their positive cones are 1-concave. In particular we show that the Banach envelope of Ces̀ro sequence space cesp(v), 0 < p < 1, coincides isometrically with the weighted l1(w) space where w(n) = ∥en∥cesp(v) = (∑ i=n∞i-pv(i)1/p and e n are the unit vectors. For Ces̀ro function space Ces p(v), 0 < p < 1, its Banach envelope Cesp(v) is isometrically equal to L1(w) with w(t) = (∫t∞ s-pv(s)ds)1/p, t ∈ (0;∞).

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Functiones et Approximatio, Commentarii Mathematici