C(X) as a (bi)dual space
Garth Dales (University of Lancaster)
Tuesday 23rd April, 2013 16:00-17:00 Maths 203
Let K be a compact space, and let C(K) be the commutative C-algebra
consisting of all complex-valued, continuous functions on K, with the uniform
norm. We shall discuss the following questions:
(I) When are two spaces C(K) and C(L) isomorphic or isometrically
(II) When is C(K) isomorphic or isometrically isomorphic to the dual of
a Banach space? If so, how unique is the predual?
(III) When is C(K) isometrically isomorphic or isomorphic to the bidual
of a Banach space?
(IV) The second dual of C(K) is C(eK), where eK is a `big' compact space
(called the hyper-Stonean envelope). How do we characterize the spaces eK?