Norm-attaining polynomials and differentiability
Volume 151 / 2002
Studia Mathematica 151 (2002), 1-21
MSC: Primary 46G25; Secondary 46B20.
DOI: 10.4064/sm151-1-1
Abstract
We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Fréchet differentiable. We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces.
