Abstract
By a system (X, T) we mean a continuous selfmap T: X → X of a separable metrizable space X and by its linearization a topological embedding i: X → E into a linear system (E, L) consisting of a Hilbert or Euclidean space E and a continuous linear operator L: E → E and satisfying the equivariancy condition L ○ i = i ○ T. Our main results concern linearization by systems (E, L) in which the norm of L is < 1. By a weakening of the equivariancy condition L ○ i = i ○ T, we show that a system which does not admit a finite dimensional linearization may still be linearized in this modified sense in a finite dimensional space.
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Janos, L. (2001). Revisiting the Celebrated Thesis of J. de Groot: “Everything is Linear.”. In: Koslowski, J., Melton, A. (eds) Categorical Perspectives. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1370-3_12
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DOI: https://doi.org/10.1007/978-1-4612-1370-3_12
Publisher Name: Birkhäuser, Boston, MA
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