ISSN:
1572-9281
Keywords:
Subspaces of Lp and ℓ p
;
linear isometries
;
distribution measures
;
equimeasurable functions
;
Banach-Mazur compactum
;
isometrically universal finite-dimensional
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We present three results on isometric embeddings of a (closed, linear) subspace X of Lp=Lp[0,1] into ℓ p . First we show that if p ∉ 2N, then X is isometrically isomorphic to a subspace of ℓ p if and only if some, equivalently every, subspace of Lp which contains the constant functions and which is isometrically isomorphic to X, consists of functions having discrete distribution. In contrast, if p ∈ 2N; and X is finite-dimensional, then X is isometrically isomorphic to a subspace of ℓ p , where the positive integer N depends on the dimension of X, on p , and on the chosen scalar field. The third result, stated in local terms, shows in particular that if p is not an even integer, then no finite-dimensional Banach space can be isometrically universal for the 2-dimensional subspaces of Lp .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009764511096
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