Pointwise domination of matrices and comparison of ℐ_pnorms

Restriction theorems for Hankel operators

“…As already mentioned, this proof does not extend to p ∈ 2N; see e.g. [9,13]. Below we give a different proof which works for all 1 ≤ p < ∞, but does not give precise information about the constants in the estimates.…”

Completely Bounded and Ideal Norms of Multiplication Operators and Schur Multipliers

“…norm and the completely 1-summing norm of Schur multipliers from S ∞ or B( 2 ) into S 1 are not equivalent. Indeed, by [20], there exist matrices φ and ψ s.t. |ψ ij | ≤ φ ij for any pair (i, j), φ ∈ S 1 , while ψ / ∈ S 1 .…”

Rank-one quantum games

“…Remark 5.6 from [31] then suggests how we can separate the values ω * (G) and V (G). Using [42], we can find matrices ϕ and ψ for which |ϕ ij | ≤ |ψ ij | for all i, j, but ϕ 1 ≫ ψ 1 . If G is the game corresponding to the Schur multiplier M ϕ , then V (G) = ϕ 2 1 but ω * (G) is bounded by the far smaller ψ 2 1 .…”