On the Complemented
نویسنده
چکیده
Rosenthal [R] introduced the Lp space Xp in 1971. Among its interesting properties are that it contains and is contained in isomorphs of lp ⊕ l2, but is not isomorphic to a complemented subspace of lp⊕ l2. These properties have made Xp rather resistant to standard approaches to classifying its complemented subspaces. For example it was first proved that Xp was primary in [JO2] where the device of simultaneously Lp, L2 bounded operators was employed to prove a version of the decomposition method for Xp. The problem really is that the lp and l2 structures in Xp are mixed in a much different way than they are in lp ⊕ l2 or ( ∑
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