A Hull with No Nontrivial Gleason Parts
Complex Variables
2016-05-16 v1
Abstract
The existence of a nontrivial polynomially convex hull with every point a one-point Gleason part and with no nonzero bounded point derivations is established. This strengthens the \hbox{celebrated} result of Stolzenberg that there exists a nontrivial polynomially convex hull that contains no analytic discs. A doubly generated counterexample to the peak point conjecture is also presented.
Keywords
Cite
@article{arxiv.1605.04020,
title = {A Hull with No Nontrivial Gleason Parts},
author = {Brian J. Cole and Swarup N. Ghosh and Alexander J. Izzo},
journal= {arXiv preprint arXiv:1605.04020},
year = {2016}
}