# nLab operator

There are different meanings of operator:

• A linear operator, or more generally an element of an operator algebra.

• In higher type theory?, an operator is a function from a set of functions to itself:

$O:{Y}^{X}\to {Y}^{X},\phantom{\rule{1em}{0ex}}O\in \left({Y}^{X}{\right)}^{{Y}^{X}}={Y}^{X×{Y}^{X}}.$O\colon Y^X \to Y^X , \quad O \in (Y^X)^{Y^X} = Y^{X \times Y^X} .
• Probably more …

The connection between these two is that, if $H$ is a vector space of functions ($H\subseteq {Y}^{X}$), then a linear operator (in the first) is a special case of a (partially defined) operator (in the second sense).

Revised on July 23, 2011 06:49:05 by Toby Bartels (76.85.192.183)