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A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing.
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Karlsson, Anders; Margulis, Gregory A. A multiplicative ergodic theorem and nonpositively curved spaces. Comm. Math. Phys. 208 (1999), no. 1, 107–123
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Handbook of metric fixed point theory. Edited by William A. Kirk and Brailey Sims. Kluwer Academic Publishers, Dordrecht, 2001. xiv+703 pp
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Karlsson, Anders, Non-expanding maps and Busemann functions. Ergodic Theory Dynam. Systems 21 (2001), no. 5, 1447–1457
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Rieffel, M.A., Group C ∗ C^{*} -algebras as compact quantum metric spaces. Doc. Math. 7 (2002), 605–651
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Karlsson, Anders; Noskov, Guennadi A. Some groups having only elementary actions on metric spaces with hyperbolic boundaries. Geom. Dedicata 104 (2004), 119–137
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Basso, Giuliano Fixed point theorems for metric spaces with a conical geodesic bicombing. Ergodic Theory Dynam. Systems 38 (2018), no. 5, 1642–1657
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Kapovich, M. and Leeb, B., Finsler bordifications of symmetric and certain locally symmetric spaces. Geometry and Topology, 22 (2018) 2533-2646
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Walsh, Cormac Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 5, 1831–1877
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Gutiérrez, Armando W.; On the Metric Compactification of Infinite-dimensional Spaces. Canad. Math. Bull. 62 (2019), no. 3, 491–507
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Caprace, Pierre-Emmanuel; Lytchak, Alexander At infinity of finite-dimensional CAT(0) spaces. Math. Ann. 346 (2010), no. 1, 1–21
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Eisner, Tanja Stability of operators and operator semigroups. Operator Theory: Advances and Applications, 209. Birkhäuser Verlag, Basel, 2010. viii+204 pp
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Cantat, Serge. Sur les groupes de transformations birationnelles des surfaces. Ann. of Math. 174(1) (2011), 299–340
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Chalendar, Isabelle; Partington, Jonathan R. Modern approaches to the invariant-subspace problem. Cambridge Tracts in Mathematics, 188. Cambridge University Press, Cambridge, 2011. xii+285 pp
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Karlsson, Anders; Ledrappier, François Noncommutative ergodic theorems. Geometry, rigidity, and group actions, 396–418, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 2011
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Bader, U.; Gelander, T.; Monod, N. A fixed point theorem for L1 spaces. Invent. Math. 189 (2012), no. 1, 143–148
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Claassens, Floris The horofunction boundary of the infinite dimensional hyperbolic space. Geom. Dedicata 207 (2020), 255–263
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Gouëzel, S., Karlsson, A.: Subadditive and multiplicative ergodic theorems. J. Eur. Math. Soc. (JEMS) 22(6), 1893–1915 (2020)
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Gutiérrez, Armando W. Characterizing the metric compactification of Lp spaces by random measures. Ann. Funct. Anal. 11 (2020), no. 2, 227–243
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Bowen, Lewis; Hayes, Ben; Lin, Yuqing, A multiplicative ergodic theorem for von Neumann algebra valued cocycles, Commun. Math. Phys. 384: 2 (2021), 1291-1350
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Gutiérrez, Armando W.; Karlsson, Anders, Comments on the cosmic convergence of nonexpansive maps. J. Fixed Point Theory Appl. 23 (2021), no. 4, Paper No. 59, 10 pp
2021
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Huang, Jingyin; Osajda, Damian Helly meets Garside and Artin. Invent. Math. 225 (2021), no. 2, 395–426
2021
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Karlsson, Anders, Hahn-Banach for metric functionals and horofunctions. J. Funct. Anal. 281 (2021), no. 2, Paper No. 109030, 17 pp
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Karlsson, Anders, From linear to metric functional analysis. Proc. Natl. Acad. Sci. USA 118 (2021), no. 28, Paper No. e2107069118, 5 pp
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2021
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Pence, Zach, Metric Spectral Theory and the Invariant Subspace Problem, Master thesis, Uppsala University, 2021
2021
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Avelin, B.; Karlsson, A. Deep limits and cut-off phenomena for neural networks, to appear in J. Machine Learning Research, 2022
2022
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Karlsson, Anders; Elements of a metric spectral theory. In: Dynamics, geometry, number theory—the impact of Margulis on modern mathematics, 276–300, Univ. Chicago Press, Chicago, IL, 2022
2022
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