Dynamics of the semigroup of contractive automorphisms of Banach spaces
Copyright policy )Dynamics of the semigroup of contractive automorphisms of Banach spaces
Motivated by some recent twaddles on Mazur rotations problem, we study the "dynamics" of the semigroup of contractive automorphisms of Banach spaces, mostly in finite-dimensional spaces. We focus on the metric aspects of the "action" of such semigroups, the size of the orbits and semitransitivity properties, and their impact on the geometry of the unit ball of the underlying space.
16 pages, 8 figures
Banach space, Hilbert space, 46B03, 46B04, 46C15, Dynamical Systems (math.DS), contractive automorphism, Functional Analysis (math.FA), Mathematics - Functional Analysis, semitransitivity, FOS: Mathematics, Isometric theory of Banach spaces, Mathematics - Dynamical Systems, Mazur rotations problem
Banach space, Hilbert space, 46B03, 46B04, 46C15, Dynamical Systems (math.DS), contractive automorphism, Functional Analysis (math.FA), Mathematics - Functional Analysis, semitransitivity, FOS: Mathematics, Isometric theory of Banach spaces, Mathematics - Dynamical Systems, Mazur rotations problem
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