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Properties of bases of some koethe spaces and their subspaces

โœ Scribed by V. P. Kondakov


Publisher
Springer US
Year
1980
Tongue
English
Weight
209 KB
Volume
14
Category
Article
ISSN
0016-2663

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We prove that if X is a Tychonoff topological space, Y a subspace of X, and every bounded continuous pseudometric on Y can be extended to a continuous pseudometric on X, then the free topological group F M (Y ) coincides with the topological subgroup of F M (X) generated by Y . For this purpose, a n

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## Abstract For ฮฉ an open subset of IR^N^ and 1 < __p__ < โˆž, we prove that any complemented subspace __E__ of __L__^p^~loc~ (ฮฉ) contains either a complemented copy of (__l__^2^)^IN^ or a complemented copy of (__l__^p^)^IN^, provided โ‰ˆ๏ธ __F__ โ‰ˆ๏ธ and ฯ‰ and โ‰ˆ๏ธ ฯ‰โŠ• __F__ with __F__ Banach space. We also