Questions about extreme points

TL;DR

This paper investigates the geometric structure of the unit ball's extreme points in specific subspaces of $L^1$ and $L^ Infty$ on the circle, focusing on functions with spectral gaps and Toeplitz operator kernels.

Contribution

It provides new insights into the structure of extreme points in these function spaces, especially with spectral constraints and operator kernels.

Findings

Characterization of extreme points in subspaces of $L^1$ and $L^ Infty$ with spectral gaps.

Analysis of extreme points in kernels of Toeplitz operators in $H^ Infty$.

Results enhance understanding of geometric properties of these function spaces.

Abstract

We discuss the geometry of the unit ball -- specifically, the structure of its extreme points (if any) -- in subspaces of $L^1$ and $L^\infty$ on the circle that are formed by functions with prescribed spectral gaps. A similar issue is considered for kernels of Toeplitz operators in $H^\infty$.