Representations of the spaces of Lipschitz functions

Wulbert, Daniel

doi:10.1016/0022-1236(74)90025-1

Cited by 4 publications

(2 citation statements)

References 6 publications

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“…De Leeuw in [9] first proved that, if 0 < α < 1, then (lip α ([0, 1])) * * is isometrically isomorphic to Lip α ([0, 1]). In (1974) Wulbert [26] extended de Leeuw's theorem to finite dimensional compact sets K (lip α (K)) * * ≃ Lip α (K) (6) Let us notice that de Leeuw identified the dual of lip α ([0, 1]) , by constructing an isometric embedding of lip α ([0, 1]) into a space C 0 (W) of continuous function on…”

Section: Introductionmentioning

confidence: 99%

Duality and distance formulas in Lipschitz-Hölder spaces

Angrisani¹,

Ascione²,

D'Onofrio³

et al. 2019

Preprint

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For a compact metric space (K, ρ), the predual of Lip(K, ρ) can be identified with the normed space M(K) of finite (signed) Borel measures on K equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of M(K) by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between Lip(K, ρ) and (lip(K, ρ)) * * [15]. In this work we also show that the pair (lip(K, ρ), Lip(K, ρ)) can be framed in the theory of o-O type structures introduced by K. M. Perfekt.

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Section: Introductionmentioning

confidence: 99%

Duality and distance formulas in Lipschitz-Hölder spaces

Angrisani¹,

Ascione²,

D'Onofrio³

et al. 2019

Preprint

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show abstract

“…c 0 (£)), E being a Banach space. In a quite different way Wulbert [16] characterised the compact metric spaces, Y, such that \ W (Y) separates points of Y and is isomorphic to c 0 . Frampton and Tromba [6] found that \ k,w (L) is isomorphic to c 0 and A k,w (L) to /°°, L being a compact C°°-Riemanian «-manifold.…”

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confidence: 99%