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  • 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.
  • 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. (en)
Title
  • On a classical renorming construction of V. Klee
  • On a classical renorming construction of V. Klee (en)
skos:prefLabel
  • On a classical renorming construction of V. Klee
  • On a classical renorming construction of V. Klee (en)
skos:notation
  • RIV/67985840:_____/12:00367447!RIV12-AV0-67985840
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  • P(IAA100190901), Z(AV0Z10190503)
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  • 1
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  • 156151
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  • RIV/67985840:_____/12:00367447
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  • rotund norm; locally uniformly rotund norm; Gateaux differentiable norm (en)
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  • US - Spojené státy americké
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  • [2DB91C9DB3CA]
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  • Journal of Mathematical Analysis and Applications
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  • 385
http://linked.open...iv/tvurceVysledku
  • Montesinos, V.
  • Zizler, Václav
  • Guirao, A. J.
http://linked.open...ain/vavai/riv/wos
  • 000294979100044
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-247X
number of pages
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  • 10.1016/j.jmaa.2011.06.059
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