Positivity

, Volume 2, Issue 4, pp 339–367

Subspaces of Lp Isometric to Subspaces of ℓp

  • F. Delbaen
  • H. Jarchow
  • A. Pełczyński
Article

DOI: 10.1023/A:1009764511096

Cite this article as:
Delbaen, F., Jarchow, H. & Pełczyński, A. Positivity (1998) 2: 339. doi:10.1023/A:1009764511096

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 .

Subspaces of Lp and ℓp linear isometries distribution measures equimeasurable functions Banach-Mazur compactum isometrically universal finite-dimensional 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • F. Delbaen
    • 1
  • H. Jarchow
    • 1
  • A. Pełczyński
    • 2
  1. 1.Department MathematikETH ZürichZürichSwitzerland E-mail: Email
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland E-mail: Email