A Hull with No Nontrivial Gleason Parts

A Hull with No Nontrivial Gleason Parts

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 celebrated result of Stolzenberg that there exists a nontrivial polynomially convex hull that contains no analytic discs...

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Veröffentlicht in:Indiana University mathematics journal 2018-01, Vol.67 (2), p.739-752
Hauptverfasser: Cole, Brian J., Ghosh, Swarup N., Izzo, Alexander J.
Format: Artikel
Sprache:eng
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Zusammenfassung: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 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.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2018.67.7300