summaryrefslogtreecommitdiffstats
path: root/pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md
diff options
context:
space:
mode:
authorJustin Gassner <justin.gassner@mailbox.org>2024-02-20 12:01:07 +0100
committerJustin Gassner <justin.gassner@mailbox.org>2024-02-20 12:01:07 +0100
commit8b9bb9346c217874670b0f1798ab6f1cb28fdb83 (patch)
tree167336a47f0d19dc8b0897f4e94be0e44933eeb2 /pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md
parent7c66b227a494748e2a546fb85317accd00aebe53 (diff)
downloadsite-8b9bb9346c217874670b0f1798ab6f1cb28fdb83.tar.zst
Update
Diffstat (limited to 'pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md')
-rw-r--r--pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md6
1 files changed, 6 insertions, 0 deletions
diff --git a/pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md b/pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md
index 1140e45..c88608b 100644
--- a/pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md
+++ b/pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md
@@ -3,6 +3,10 @@ title: Uniform Boundedness Theorem
parent: The Fundamental Four
grand_parent: Functional Analysis Basics
nav_order: 2
+description: >
+ The Uniform Boundedness Theorem states that a pointwise bounded collection of
+ bounded linear operators from a Banach space into a normed space must be
+ uniformly bounded. We give a proof based on Baire’s Category Theorem.
---
# {{ page.title }}
@@ -84,7 +88,9 @@ $$
If $X$ is not complete, this may be false.
+{% comment %}
TODO:
- strong operator convergence
- Kreyszig 4.9-5
- Haase 15.6
+{% endcomment %}