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Finitely additive measures and complementability of Lipschitz-free spaces

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Abstract

We prove in particular that the Lipschitz-free space over a finite-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is 1. As a tool to obtain the main result we establish several facts on the structure of finitely additive measures on finite-dimensional spaces.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Marek Cúth, Ondřej F. K. Kalenda & Petr Kaplický

Authors
  1. Marek Cúth
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  2. Ondřej F. K. Kalenda
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  3. Petr Kaplický
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Corresponding author

Correspondence to Ondřej F. K. Kalenda.

Additional information

M. Cúth is a junior researcher in the University Center for Mathematical Modelling, Applied Analysis and Computational Mathematics (MathMAC). M. Cúth and O. Kalenda were supported in part by the grant GAČR 17-00941S. P. Kaplický is a member of the Nečas Center for Mathematical Modeling.

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Cúth, M., Kalenda, O.F.K. & Kaplický, P. Finitely additive measures and complementability of Lipschitz-free spaces. Isr. J. Math. 230, 409–442 (2019). https://doi.org/10.1007/s11856-019-1829-y

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  • DOI: https://doi.org/10.1007/s11856-019-1829-y

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