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We show that the Hilbert space is coarsely embeddable into any for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into are equivalent for 1 ≤ p < 2.
Piotr W. Nowak. "On coarse embeddability into $ℓ_p$-spaces and a conjecture of Dranishnikov." Fundamenta Mathematicae 189.2 (2006): 111-116. <http://eudml.org/doc/282754>.
@article{PiotrW2006, abstract = {We show that the Hilbert space is coarsely embeddable into any $ℓ_p$ for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into $ℓ_p$ are equivalent for 1 ≤ p < 2.}, author = {Piotr W. Nowak}, journal = {Fundamenta Mathematicae}, keywords = {coarse embedding; Property A; Novikov conjecture}, language = {eng}, number = {2}, pages = {111-116}, title = {On coarse embeddability into $ℓ_p$-spaces and a conjecture of Dranishnikov}, url = {http://eudml.org/doc/282754}, volume = {189}, year = {2006}, }
TY - JOUR AU - Piotr W. Nowak TI - On coarse embeddability into $ℓ_p$-spaces and a conjecture of Dranishnikov JO - Fundamenta Mathematicae PY - 2006 VL - 189 IS - 2 SP - 111 EP - 116 AB - We show that the Hilbert space is coarsely embeddable into any $ℓ_p$ for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into $ℓ_p$ are equivalent for 1 ≤ p < 2. LA - eng KW - coarse embedding; Property A; Novikov conjecture UR - http://eudml.org/doc/282754 ER -