Smooth symmetric bilinear forms on ${\mathcal L}_s(^2l_{\infty}^2)$

Abstract

In [Carpathian Math. Publ. 2020, 12 (2), 340-352], the author classified the extreme points and exposed points of the unit ball of the space of symmetric bilinear forms on the space ${\mathcal L}_s(^2l_{\infty}^2)$, where ${\mathcal L}_s(^2l_{\infty}^2)$ is the space of symmetric bilinear forms on the plane with the supremum norm. Motivated by this paper, we classify the smooth points of the unit ball of the space of symmetric bilinear forms on ${\mathcal L}_s(^2l_{\infty}^2).$