By Caixing Gu and Jonathan E. Shapiro

This paper appears in the Proceedings of the American Mathematical
Society, Volume **131,** Number 9 (2003), 2779-2789.

You can see it on their web site here.

**Abstract:**

We find some extreme points in the unit ball of the set of Hankel operators
and show that the unit ball of the set of compact Hankel operators
is strictly convex. We use this result to show that the collection
of *NxN* lower triangular Toeplitz contractions is strictly
convex. We also find some extreme points in certain reduced Cowen sets
and discuss cases in which they are or are not strictly convex.

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