Finitely additive measures and complementability of Lipschitz-free spaces
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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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- G. Bouchitté, T. Champion and C. Jimenez, Completion of the space of measures in the Kantorovich norm, Rivisita de Matematica della Università di Parma 4* (2005), 127–139.Google Scholar
- J. Diestel and J. J. Uhl, Jr., Vector Measures, Mathematical Surveys, Vol. 15, American Mathematical Society, Providence, RI, 1977.Google Scholar
- G. P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations. Vol. I. Linearized Steady Problems, Springer Tracts in Natural Philosophy, Vol. 38, Springer-Verlag, New York, 1994.Google Scholar
- F. John, Extremum problems with inequalities as subsidiary conditions, in Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience, New York, 1948, pp. 187–204.Google Scholar