No greedy bases for matrix spaces with mixed ℓₚ and ℓq norms

الأصل · EN

We show that non of the spaces (ₙ₌₁∞ℓₚ)ℓq, 1≤ p= q<∞, have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprect. Similarly, the spaces (ₙ₌₁∞ℓₚ)c₀, 1≤ p<∞, and (ₙ₌₁∞ cₒ)ℓq, 1≤ q<∞, do not have greedy bases. It follows from that and known results that a class of Besov spaces on ⁿ lack greedy bases as well.