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Feb 18 at 6:37 comment added PPB It looks like the mentioned norm is the supremum norm; then, it will not be a smooth norm on $\mathbb{R}^2$.
Feb 18 at 6:23 comment added PPB I also want to construct such renorming in case of an infinite dimensional Banach space; any hints, please? Can I simply define the $\ell_2$ direct sum of the mentioned norm with a Hilbert space? Will that work? Any other suggestions would also appreciated.
Feb 18 at 6:14 vote accept PPB
Feb 16 at 21:34 comment added user479223 @LSpice It is indeed the same as "compactly LUR."
Feb 16 at 21:33 comment added LSpice Re, it is not, although I see now that it is used. Is it the same as "compactly LUR"?
Feb 16 at 21:32 comment added user479223 @LSpice It is defined in the question.
Feb 16 at 21:32 comment added LSpice What is CLUR?..
Feb 16 at 14:21 history edited user479223 CC BY-SA 4.0
deleted 4 characters in body
Feb 16 at 14:12 history answered user479223 CC BY-SA 4.0