cotype

Noun

cotype (plural cotypes)

1. (dated) A syntype or paratype.
2. (functional analysis) A Banach space (X,‖·‖), such that, given a sequence of independent random variables from a Rademacher distribution, (εᵢ), and a rank q in the range from 2 to infinity, there exists a finite constant C≥1 such that for all finite sequences (x_i)∈X, 𝔼_ε[‖∑ limits ᵢ₌₁ⁿεᵢx_i‖^q]≥1/(C^q)(∑ limits ᵢ₌₁ⁿ‖x_i‖^q), if;2≤q<∞ or 𝔼_ε[‖∑ limits ᵢ₌₁ⁿεᵢx_i‖]≥1/C sup ‖x_i‖, if;q=∞ .