cotype

English

Etymology

From co- +‎ type.

Noun

cotype (plural cotypes)

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

   Coordinate term: type

Anagrams

• ectopy