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Extreme and exposed representing measures of the disk algebra

100%

Heinis A., Wiegerinck J.

Annales Polonici Mathematici

2000

tom 73

nr 2

105-118

We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed and show that so-called BSZ-measures are never exposed.

Exposed points in the set of representing measures for the disc algebra

100%

Izzo A.

Annales Polonici Mathematici

1995

tom 61

nr 1

59-62

It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Heinis A.

1 Izzo A.

1 Wiegerinck J.

1 2000

1 1995

Wyniki wyszukiwania

Extreme and exposed representing measures of the disk algebra

Exposed points in the set of representing measures for the disc algebra