For more of these summaries, you can search this blog for “Latest posts on my Blogger blog”, or directly see https://explainingmaths.wordpress.com/?s=%22Latest+posts+on+my+Blogger+blog%22
Here are some links to my most recent posts on my Blogger blog, where I am able to use MathJax.
I’ll periodically post updates on this blog, with links and brief descriptions.
My latest set of posts is a series of 6 posts (intended for mathematics undergraduates in their 3rd or 4th year) on the Hahn-Banach extension theorem for continuous linear functionals on normed spaces.
Date | Title and link | Description |
7/4/24 | An introduction to the Hahn-Banach extension theorem: Part VI | Proof of the real Hahn-Banach theorem using transfinite induction (some details left to the reader). |
6/4/24 | An introduction to the Hahn-Banach extension theorem: Part V | Proof of the real Hahn-Banach theorem using Zorn’s Lemma |
2/4/24 | An introduction to the Hahn-Banach extension theorem: Part IV | How every complex normed space is also a real normed space, and how the complex and real dual spaces are related. Deduction of the complex Hahn-Banach theorem from the real Hahn-Banach theorem. |
1/4/24 | An introduction to the Hahn-Banach extension theorem: Part III | The Hahn-Banach Extension Theorem for linear functionals on separable, real normed spaces, proved using the key lemma and (at the end) extension to the closure. |
31/3/24 | An introduction to the Hahn-Banach extension theorem: Part II | – A look at the operator norm for bounded linear functionals on real normed spaces. – The key lemma used to extend bounded linear functionals on real normed spaces by one dimension without increasing the operator norm. |
31/3/24 | An introduction to the Hahn-Banach extension theorem: Part I | The statement of the Hahn-Banach extension theorem for bounded linear functionals on normed spaces, along with some initial comments about how we can approach the proof. |