Abstract
AbstractWe show that each infinite-dimensional reflexive Banach space $$(X,\left\| \cdot \right\| _X)$$
(
X
,
·
X
)
has an equivalent norm $$\left\| \cdot \right\| _{X,0}$$
·
X
,
0
such that $$(X,\left\| \cdot \right\| _{X,0})$$
(
X
,
·
X
,
0
)
is LUR and contains a diametrically complete set with empty interior. We also prove that after a suitable equivalent renorming, the Banach space $$C([0,1],{\mathbb {R}})$$
C
(
[
0
,
1
]
,
R
)
contains a constant width set with empty interior.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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