Cotype

English

Etymology

From Template:Prefix.

Noun

1. Template:Lb A syntype or paratype.
2. Template:Lb A Banach space $(X,\Vert \cdot \Vert )$, such that, given a sequence of independent random variables from a Rademacher distribution, $({\epsilon }_i)$, and a rank $q$ in the range from 2 to infinity, there exists a finite constant $C\ge 1$ such that for all finite sequences $(x_i)\in X$, ${𝔼}_{\epsilon }\left[{\Vert \sum _{i=1}^n{\epsilon }_i{x}_i\Vert }^q\right]\ge \frac{1}{C^q}(\sum _{i=1}^n\Vert x_i{\Vert }^q),\text{if}2\le q<\mathrm{\infty }$ or ${𝔼}_{\epsilon }\left[\Vert \sum _{i=1}^n{\epsilon }_i{x}_i\Vert \right]\ge \frac{1}{C}\sup \Vert x_i\Vert ,\text{if}q=\mathrm{\infty }$ .

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