---
tag: 03TM135G0N
kind: concept
name: Continuous linear map
aliases: [bounded-linear-operator, bounded-operator]
msc: [47B01]
sources:
  - url: https://en.wikipedia.org/wiki/Bounded_operator
    locator: lead section
---

## Summary

A continuous linear map between normed spaces is a linear map that is continuous for the norm topologies.
Such maps are the same as the bounded linear maps, which multiply lengths by at most a fixed constant.