Geodesic
On the Metric Compactification of Infinite-dimensional $\ell _{p}$ Spaces
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 491-507

Voir la notice de l'article provenant de la source Cambridge University Press

The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell _{p}$ spaces for all $1\leqslant p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.
DOI : 10.4153/S0008439518000681
Mots-clés : metric compactification, horofunction compactification, metric functional, Banach space 
Gutiérrez, Armando W. On the Metric Compactification of Infinite-dimensional $\ell _{p}$ Spaces. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 491-507. doi: 10.4153/S0008439518000681
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000681/}
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[1] Ballmann, W., Lectures on spaces of nonpositive curvature , DMV Seminar, 25, Birkhäuser Verlag, Basel, 1995. . Google Scholar | DOI

[2] Ballmann, W., Gromov, M., and Schroeder, V., Manifolds of nonpositive curvature , Progress in Mathematics, 61, Birkhäuser Boston, Inc., Boston, MA, 1985. . Google Scholar | DOI

[3] Bridson, M. R. and Haefliger, A., Metric spaces of non-positive curvature , Grundlehren der Mathematischen Wissenschaften, 319, Springer-Verlag, Berlin, 1999. . Google Scholar | DOI

[4] Clarkson, J. A., Uniformly convex spaces . Trans. Amer. Math. Soc. 40(1936), 396–414. . Google Scholar | DOI

[5] Friedland, S. and Freitas, P. J., p-metrics on GL(n, ℂ)/U and their Busemann compactifications . Linear Algebra Appl. 376(2004), 1–18. . Google Scholar | DOI

[6] Gaubert, S. and Vigeral, G., A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces . Math. Proc. Cambridge Philos. Soc. 152(2012), 341–363. . Google Scholar | DOI

[7] Gouëzel, S. and Karlsson, A., Subadditive and multiplicative ergodic theorems. 2015. arxiv:1509.07733. Google Scholar

[8] Gromov, M., Hyperbolic manifolds, groups and actions . In: Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) , Ann. of Math. Stud., 97, Princeton University Press, Princeton, NJ, 1981, pp. 183–213. Google Scholar

[9] Gutiérrez, A. W., The horofunction boundary of finite-dimensional ℓ spaces . Colloq. Math. 155(2019), 51–65. . Google Scholar | DOI

[10] Ji, L. and Schilling, A.-S., Polyhedral horofunction compactification as polyhedral ball. 2016. arxiv:1607.00564. Google Scholar

[11] Karlsson, A., Metz, V., and Noskov, G. A., Horoballs in simplices and Minkowski spaces . Int. J. Math. Math. Sci. pages Art. 2006, 23656. . Google Scholar | DOI

[12] Karlsson, A., Dynamics of Hilbert nonexpansive maps . In: Handbook of Hilbert geometry , IRMA Lect. Math. Theor. Phys., 22, Eur. Math. Soc., Zürich, 2014, pp. 263–273. Google Scholar

[13] Karlsson, A. and Ledrappier, F., Noncommutative ergodic theorems . In: Geometry, rigidity, and group actions , Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 2011, pp. 396–418. Google Scholar

[14] Kelley, J. L., General topology. Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.], Graduate Texts in Mathematics, 27, Springer-Verlag, New York-Berlin, 1975. Google Scholar

[15] Khamsi, M. A. and Kirk, W. A., An introduction to metric spaces and fixed point theory , Pure and Applied Mathematics (New York), Wiley-Interscience, New York, 2001. . Google Scholar | DOI

[16] Maher, J. and Tiozzo, G., Random walks on weakly hyperbolic groups . J. Reine Angew. Math. 742(2018), 187–239. . Google Scholar | DOI

[17] Rieffel, M. A., Group C ∗-algebras as compact quantum metric spaces . Doc. Math. 7(2007), 605–651. Google Scholar

[18] Walsh, C., The horofunction boundary of finite-dimensional normed spaces . Math. Proc. Cambridge Philos. Soc. 142(2007), 497–507. . Google Scholar | DOI

[19] Walsh, C., Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces. 2016. arxiv:1610.07508. Google Scholar

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