Banach-Steinhaus theorem
Let be a Banach space and a normed space. If a family of bounded operators from to satisfies
for each , then
i.e. is a bounded subset of with the usual operator norm. In other words, there exists a constant such that for all and ,
Title | Banach-Steinhaus theorem |
---|---|
Canonical name | BanachSteinhausTheorem |
Date of creation | 2013-03-22 14:48:39 |
Last modified on | 2013-03-22 14:48:39 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 5 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 46B99 |
Synonym | Principle of Uniform Boundedness |
Synonym | Uniform Boundedness Principle |