# Bounded linear operator

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Bounded linear operator](https://ocme.evemisslab.com/en/atlas/atlas-bounded-linear-operator/)

A linear map between normed spaces is bounded when one nonnegative constant uniformly controls all output norms relative to input norms.

atlas-bounded-linear-operator · canonical_mko

[Bounded linear operator](https://ocme.evemisslab.com/en/mko/mko-bounded-linear-operator/)

## Prerequisite nodes


- [Linear map between real vector spaces](https://ocme.evemisslab.com/en/atlas/atlas-general-linear-map/)
- [Real normed vector space](https://ocme.evemisslab.com/en/atlas/atlas-real-normed-vector-space/)
- [Usual order on the real numbers](https://ocme.evemisslab.com/en/atlas/atlas-order-relation/)