Isomorphism of certain weak L p spaces

Denny Leung

Studia Mathematica (1993)

  • Volume: 104, Issue: 2, page 151-160
  • ISSN: 0039-3223

Abstract

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It is shown that the weak L p spaces ℓ p , ∞ , L p , ∞ [ 0 , 1 ] , and L p , ∞ [ 0 , ∞ ) are isomorphic as Banach spaces.

How to cite

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Leung, Denny. "Isomorphism of certain weak $L^{p}$ spaces." Studia Mathematica 104.2 (1993): 151-160. <http://eudml.org/doc/215966>.

@article{Leung1993,
abstract = {It is shown that the weak $L^p$ spaces $ℓ^\{p,∞\}, L^\{p,∞\}[0,1]$, and $L^\{p,∞\}[0,∞)$ are isomorphic as Banach spaces.},
author = {Leung, Denny},
journal = {Studia Mathematica},
keywords = {weak spaces},
language = {eng},
number = {2},
pages = {151-160},
title = {Isomorphism of certain weak $L^\{p\}$ spaces},
url = {http://eudml.org/doc/215966},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Leung, Denny
TI - Isomorphism of certain weak $L^{p}$ spaces
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 2
SP - 151
EP - 160
AB - It is shown that the weak $L^p$ spaces $ℓ^{p,∞}, L^{p,∞}[0,1]$, and $L^{p,∞}[0,∞)$ are isomorphic as Banach spaces.
LA - eng
KW - weak spaces
UR - http://eudml.org/doc/215966
ER -

References

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  1. [1] N. L. Carothers and S. J. Dilworth, Subspaces of L p , q , Proc. Amer. Math. Soc. 104 (1988), 537-545. 
  2. [2] D. H. Leung, L p , ∞ has a complemented subspace isomorphic to ℓ 2 , Rocky Mountain J. Math. 22 (1992), 943-952. 
  3. [3] D. H. Leung, Embedding L p , ∞ into L p , ∞ [ 0 , 1 ] complementably, Bull. London Math. Soc. 23 (1991), 583-586. 
  4. [4] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin 1977. Zbl0362.46013
  5. [5] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, Berlin 1979. Zbl0403.46022

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