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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 %} |