8 citations · 18 across the 4 of their papers we have counts for
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-smooth approximations of LUR norms
Petr Hajek, Antonin Prochazka
Let be a WCG Banach space admitting a -Fr\' echet smooth norm. Then admits an equivalent norm which is simultaneously -Fr\' echet smooth, LUR, and a uniform limit…
Weak dentability index of spaces
Petr Hajek, Gilles Lancien, Antonin Prochazka
We compute the weak-dentability index of the spaces where is a countable compact space. Namely , whenever . More general…
Mazur intersection property for Asplund spaces
Miroslav Bacak, Petr Hajek
The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density chara…
Smooth norms and approximation in Banach spaces of the type C(K)
Petr Hajek, Richard Haydon
We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, th…