Tight Embeddability of Proper and Stable Metric Spaces

F. Baudier; G. Lancien

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 140-156, electronic only
  • ISSN: 2299-3274

Abstract

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We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.

How to cite

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F. Baudier, and G. Lancien. "Tight Embeddability of Proper and Stable Metric Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 140-156, electronic only. <http://eudml.org/doc/270830>.

@article{F2015,
abstract = {We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.},
author = {F. Baudier, G. Lancien},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {almost Lipschitz embeddability; nearly isometric embeddability; proper metric spaces; stable metric spaces; Lipschitz embeddability},
language = {eng},
number = {1},
pages = {140-156, electronic only},
title = {Tight Embeddability of Proper and Stable Metric Spaces},
url = {http://eudml.org/doc/270830},
volume = {3},
year = {2015},
}

TY - JOUR
AU - F. Baudier
AU - G. Lancien
TI - Tight Embeddability of Proper and Stable Metric Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 140
EP - 156, electronic only
AB - We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.
LA - eng
KW - almost Lipschitz embeddability; nearly isometric embeddability; proper metric spaces; stable metric spaces; Lipschitz embeddability
UR - http://eudml.org/doc/270830
ER -

References

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