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On Subspaces of the Spaces L and of Their Strong Duals

✍ Scribed by Angela A. Albanese

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
660 KB
Volume
197
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For Ξ© an open subset of IR^N^ and 1 < p < ∞, we prove that any complemented subspace E of L^p^~loc~ (Ξ©) contains either a complemented copy of (l^2^)^IN^ or a complemented copy of (l^p^)^IN^, provided β‰ˆοΈ F β‰ˆοΈ and Ο‰ and β‰ˆοΈ Ο‰βŠ• F with F Banach space. We also prove that any complemented subspace E of (L^p^~loc~(Ξ©))^1^~Ξ²~ contains either a complemented copy of (l^2^)^(IN)^ or a complemented copy of (l^p^)^(IN)^, provided E β‰ˆοΈ F, β‰ˆοΈ Ο€ and β‰ˆοΈ Ο€ βŠ• F with F Banach space.

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