On a classical renorming construction of V. Klee

0367447 - MÚ 2012 RIV US eng J - Journal Article
Guirao, A. J. - Montesinos, V. - Zizler, Václav
On a classical renorming construction of V. Klee.
Journal of Mathematical Analysis and Applications. Roč. 385, č. 1 (2012), s. 458-465. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA AV ČR IAA100190901
Institutional research plan: CEZ:AV0Z10190503
Keywords : rotund norm * locally uniformly rotund norm * Gateaux differentiable norm
Subject RIV: BA - General Mathematics
Impact factor: 1.050, year: 2012
http://www.sciencedirect.com/science/article/pii/S0022247X1100607X

We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X admits an equivalent norm vertical bar . vertical bar which is Frechet differentiable, locally uniformly rotund, its dual norm vertical bar . vertical bar* is uniformly Gateaux differentiable, the weak* and the norm topologies coincide on the sphere of (X*, vertical bar . vertical bar*) and, yet, vertical bar . vertical bar* is not rotund. This proves (a stronger form of) a conjecture of V. Klee.
Permanent Link: http://hdl.handle.net/11104/0202137