Subspaces of Lp Isometric to Subspaces of ℓp View Full Text


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Article Info

DATE

1998-12

AUTHORS

F. Delbaen, H. Jarchow, A. Pełczyński

ABSTRACT

We present three results on isometric embeddings of a (closed, linear) subspace X of Lp=Lp[0,1] into ℓp . First we show that if p ∉ 2N, then X is isometrically isomorphic to a subspace of ℓp 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 ℓp, 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 . More... »

PAGES

339-367

References to SciGraph publications

  • 1989-07. Approximation of zonoids by zonotopes in ACTA MATHEMATICA
  • 1974-03. Continuation of Lp-isometries in JOURNAL OF MATHEMATICAL SCIENCES
  • 1960-06. Polyhedral sections of convex bodies in ACTA MATHEMATICA
  • 1970-03. On the boundary spectrum of contractions in Minkowski spaces in SIBERIAN MATHEMATICAL JOURNAL
  • 1929-12. Über Krümmung und Windung geschlossener Raumkurven in MATHEMATISCHE ANNALEN
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    http://scigraph.springernature.com/pub.10.1023/a:1009764511096

    DOI

    http://dx.doi.org/10.1023/a:1009764511096

    DIMENSIONS

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