MathDB2 problems
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The dense-invertibles proper-Shilov-boundary conjecture
Dense-invertibles proper-Shilov-boundary conjecture. No uniform algebra with dense invertible group can have a proper Shilov boundary.
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The Stolzenberg conjecture on analytic structure in maximal ideal spaces
Stolzenberg's conjecture. Whenever a uniform algebra has proper Shilov boundary, its maximal ideal space must contain analytic structure.