✦ LIBER ✦

The Distance from l to a Subspace of Lp

✍ Scribed by D. R. Lewis

Publisher: John Wiley and Sons
Year: 1984
Tongue: English
Weight: 242 KB
Volume: 119
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19841190118

No coin nor oath required. For personal study only.

✦ Synopsis

For ( p -2) (r-2)-=0 andB any n-dimensional subspaw of an Lppace, the BANAVH-MAWR distance from Z : to E' is at most cn"(1og n)P, where ct is the natural exponent a --I 1 1 1 =mas { -i. 1 , -I ) and fi depends on p nud r.

'For E and F normed spaces the BANACH-MAZUR distance from E to F is defined to be d(E. F) =inf llull 11u-111. with the infimum taken over all isomorphisms 11 : R --

+F. The space 1; means Rn under the norm

The main result of this paper (Theorem 2) is an upper estimate for t.he distaiwe from 2 ; to an arhitrary n dimensional subspace of Lp which is optimal except for :t logarithmir factor. The result supjmrts the conjecture that

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