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author | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-20 12:01:07 +0100 |
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committer | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-20 12:01:07 +0100 |
commit | 8b9bb9346c217874670b0f1798ab6f1cb28fdb83 (patch) | |
tree | 167336a47f0d19dc8b0897f4e94be0e44933eeb2 /pages/functional-analysis-basics/the-fundamental-four | |
parent | 7c66b227a494748e2a546fb85317accd00aebe53 (diff) | |
download | site-8b9bb9346c217874670b0f1798ab6f1cb28fdb83.tar.zst |
Update
Diffstat (limited to 'pages/functional-analysis-basics/the-fundamental-four')
-rw-r--r-- | pages/functional-analysis-basics/the-fundamental-four/uniform-boundedness-theorem.md | 6 |
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 %} |