View source for Cotype

==English==
{{wp|type and cotype of a Banach space}}

===Etymology===
From {{prefix|en|co|type}}.

===Noun===
{{en-noun}}

# {{lb|en|taxonomy|dated}} A [[syntype]] or [[paratype]].
# {{lb|en|functional analysis}} A [[Banach space]] <math>(X,\|\cdot\|)</math>, such that, given a [[sequence]] of [[independent]] [[random variable]]s from a [[Rademacher distribution]], <math>(\varepsilon_i)</math>, and a rank <math>q</math> in the range from 2 to [[infinity]], there exists a [[finite]] [[constant]] <math>C \geq 1</math> such that for all finite sequences <math>(x_i) \in X</math>, <math>\mathbb{E}_{\varepsilon}\left[\left\|\sum\limits_{i=1}^n \varepsilon_i x_i\right\|^q \right]\geq \frac{1}{C^q}\left(\sum\limits_{i=1}^n \|x_i\|^q\right), \quad\text{if}\;2\leq q <\infty</math> or <math>\mathbb{E}_{\varepsilon}\left[\left\|\sum\limits_{i=1}^n \varepsilon_i x_i\right\| \right]\geq \frac{1}{C}\sup\|x_i\|, \quad\text{if}\;q=\infty</math> .
#: {{cot|en|type}}

===Anagrams===
* {{anagrams|en|a=ceopty|ectopy}}