l ∞ /c 0 has no Equivalent Strictly Convex Norm

1980 ◽  
Vol 78 (2) ◽  
pp. 225 ◽  
Author(s):  
J. Bourgain

2000 ◽  
Vol 75 (4) ◽  
pp. 445-463 ◽  
Author(s):  
Said Bahi ◽  
V. P. Sreedharan




1983 ◽  
Vol 33 (3) ◽  
pp. 213-215 ◽  
Author(s):  
M. I. Kadets ◽  
V. P. Fonf


2013 ◽  
Vol 161 (4-5) ◽  
pp. 642-649
Author(s):  
Antonio J. Lozano ◽  
Juan A. Mesa ◽  
Frank Plastria


1993 ◽  
Vol 73 (2) ◽  
pp. 180-198 ◽  
Author(s):  
R.W. Owens ◽  
V.P. Sreedharan




2020 ◽  
Vol 200 ◽  
pp. 112049
Author(s):  
Wojciech Górny


1999 ◽  
Vol 129 (6) ◽  
pp. 1107-1114 ◽  
Author(s):  
M. D. Acosta

We show that no infinite-dimensional Banach space provided with a strictly convex norm satisfies Lindenstrauss's property B. This is a generalization of previous results by Lindenstrauss for rotund spaces isomorphic to C0 and by Gowers for ℓp (1 < p < ∞). Also, there is an appropriate complex version of the announced result that works for all the C-strictly convex spaces. As a consequence, the Hardy space H1, any infinite-dimensional complex L1(μ), and, in general, any infinite-dimensional predual of a von Neumann algebra lacks Lindenstrauss's property B.





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