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Abstract
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Megrelishvili (2001) defines
light groups of isomorphisms of a Banach space as the
groups on which the weak and strong operator topologies coincide, and proves that
every bounded group of isomorphisms of Banach spaces with the point of continuity
property (PCP) is light. We investigate this concept for isomorphism groups
of classical
Banach spaces
without the PCP, specially isometry groups, and relate it to the existence of
-invariant LUR or strictly
convex renormings of
.
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Keywords
groups of isomorphisms of Banach spaces, isometry groups,
LUR renormings, renormings of Banach spaces, light groups,
invariant renormings
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Mathematical Subject Classification 2010
Primary: 22F50, 46B03
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Milestones
Received: 21 December 2017
Revised: 25 May 2018
Accepted: 26 September 2018
Published: 16 September 2019
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