A note on equivalence relations ℓp(ℓq). Issue 6 (26th October 2015) - Gao, Su; Yin, Zhi
Abstract : We consider the equivalence relations on R ω × ω induced by the Banach subspaces ℓ p ( ℓ q ) . We show that if r > p ≥ q ≥ 1, then there is no Borel reduction from the equivalence relation X ω / ℓ r ( X ), where X is a Banach space, to R ω × ω / ℓ p ( ℓ q ) .