An obstruction to ℓ p -dimension

Nicolas Monod[1]; Henrik Densing Petersen[2]

  • [1] École Polytechnique Fédérale de Lausanne Station 8, CH-1015 Lausanne (Switzerland)
  • [2] University of Copenhagen Department of Mathematical Sciences Universitetsparken 5 2100 København Ø(Denmark)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 4, page 1363-1371
  • ISSN: 0373-0956

Abstract

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Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < ∞ . We construct an exhaustion of ℓ p G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to ℓ p -dimension and gives an answer to a question of Gaboriau.

How to cite

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Monod, Nicolas, and Petersen, Henrik Densing. "An obstruction to $\ell ^{p}$-dimension." Annales de l’institut Fourier 64.4 (2014): 1363-1371. <http://eudml.org/doc/275442>.

@article{Monod2014,
abstract = {Let $G$ be any group containing an infinite elementary amenable subgroup and let $2&lt;p&lt;\infty $. We construct an exhaustion of $\ell ^pG$ by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to $\ell ^p$-dimension and gives an answer to a question of Gaboriau.},
affiliation = {École Polytechnique Fédérale de Lausanne Station 8, CH-1015 Lausanne (Switzerland); University of Copenhagen Department of Mathematical Sciences Universitetsparken 5 2100 København Ø(Denmark)},
author = {Monod, Nicolas, Petersen, Henrik Densing},
journal = {Annales de l’institut Fourier},
keywords = {$\ell ^p$-dimension; abstract harmonic analysis; -dimension},
language = {eng},
number = {4},
pages = {1363-1371},
publisher = {Association des Annales de l’institut Fourier},
title = {An obstruction to $\ell ^\{p\}$-dimension},
url = {http://eudml.org/doc/275442},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Monod, Nicolas
AU - Petersen, Henrik Densing
TI - An obstruction to $\ell ^{p}$-dimension
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 4
SP - 1363
EP - 1371
AB - Let $G$ be any group containing an infinite elementary amenable subgroup and let $2&lt;p&lt;\infty $. We construct an exhaustion of $\ell ^pG$ by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to $\ell ^p$-dimension and gives an answer to a question of Gaboriau.
LA - eng
KW - $\ell ^p$-dimension; abstract harmonic analysis; -dimension
UR - http://eudml.org/doc/275442
ER -

References

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