A doubly generated uniform algebra with a one-point Gleason part off its Shilov boundary

Izzo, Alexander J.

doi:10.4064/sm190224-7-6

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Gleason Parts In Polynomial Hulls1

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“…We then carry out the passage from A to the final desired uniform algebra B via a modification of the method used by Garnett. Both the construction of the initial uniform algebra A and the passage from A to B rely heavily on the first author's papers [16] and [18].…”

Section: Gleason Parts In Polynomial Hullsmentioning

confidence: 99%

Topology of Gleason Parts in Maximal Ideal Spaces with no Analytic Discs

Izzo¹,

Papathanasiou²

2019

Can. J. Math.-J. Can. Math.

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We strengthen, in various directions, the theorem of Garnett that every σ-compact, completely regular space X occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ideal space contains no analytic discs. We show that when the space X is metrizable, the uniform algebra can be chosen so that its maximal ideal space is metrizable as well. We also show that for every locally compact subspace X of a Euclidean space, there is a compact set K in some C N so that K \ K contains a Gleason part homeomorphic to X and K contains no analytic discs.

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Section: Gleason Parts In Polynomial Hullsmentioning

confidence: 99%