Attainment and (sub)differentiability of the infimal/supremal convolution of a function and of the square of the norm

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Speaker: 

Fabian, Marian

Affiliation: 
Mathematical Institute, Czech Academy of Science, Czech Republic

Abstract

Let TeX Embedding failed! be a Banach space whose norm is LUR and Gateaux
(Fr\'echet) smooth. Under some mild assumptions, it is shown that the
infimal/supremal convolution of a fairly general function on TeX Embedding failed! and the
square of the norm is strongly attained, and hence
Gateaux (Fr\'echet) differentiable at points of a residual set. This
contains recent results
of P. Bandyopadhayay and S. Dutta on distance and farthest distance
functions.

References.

R. Cibulka, M. Fabian, TeX Embedding failed! TeX Embedding failed!,
TeX Embedding failed!

R. Cibulka, M. Fabian, TeX Embedding failed!
TeX Embedding failed!, TeX Embedding failed!

Video: 

Details

Date & Time: 
Wednesday, May 18, 2011 - 10:45 - 11:15
Venue/Room: 
ASB 10900