Abstract
Let A be a nest algebra and K the ideal of compact operators in L(H). We ask whether or not the closed unit ball of \(\frac{{L(H)}} {{A + K}}\) has any extreme points and find that the answer depends on the structure of the nest involved. For nests with order type of the extended integers and finite dimensional atoms, we completely characterize the extreme points and show that the closed convex hull of these is not all of Ball \(\left( {\frac{{L(H)}} {{A + K}}} \right)\).
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