Arkiv för Matematik

  • Ark. Mat.
  • Volume 40, Number 2 (2002), 363-382.

Sobolev spaces in several variables in L1-type norms are not isomorphic to Banach lattices

Aleksander Pełczyński and Michał Wojciechowski

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Abstract

A Sobolev space in several variables in an L1-type norm is not complemented in its second dual. Hence it is not isomorphic as a Banach space to any complemented subspace of a Banach lattice.

Note

Both authors were supported in part by the Polish KBN grant 2P03A 036 14.

Article information

Source
Ark. Mat., Volume 40, Number 2 (2002), 363-382.

Dates
Received: 16 May 2001
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898775

Digital Object Identifier
doi:10.1007/BF02384541

Mathematical Reviews number (MathSciNet)
MR1948070

Zentralblatt MATH identifier
1021.46026

Rights
2002 © Institut Mittag-Leffler

Citation

Pełczyński, Aleksander; Wojciechowski, Michał. Sobolev spaces in several variables in L 1 -type norms are not isomorphic to Banach lattices. Ark. Mat. 40 (2002), no. 2, 363--382. doi:10.1007/BF02384541. https://projecteuclid.org/euclid.afm/1485898775


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