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We say that a Banach space
is ‘nice’ if every extreme operator from any Banach space into
is a nice operator (that is, its adjoint preserves extreme points). We prove that if
is a nice almost
is isometrically isomorphic to
for some set
. We also show that if
is a nice Banach space whose closed unit ball has the Krein–Milman property, then
. The proof of our results relies on the structure topology.
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