The Most Powerful Theorem in Operator Theory

DIBEOS December 20, 2025
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We're Luca & Sophia Di Beo. Luca is an ex-PhD Math student from the University of Udine, Italy, with a degree in Physics at the University of São Paulo (USP), Brazil, and a Master’s degree in Mathematics at the University of Kyiv, Ukraine. He writes all of the explanations and scripts. Sophia has an MA in History, from Northumbria University in the UK. She is responsible for all of the animations that you see in our videos. Our goal is to be the #1 math channel in the world. Please, give us your feedback, and help us achieve this ambitious dream. Ask for any video or course about any topic related to Mathematics & Mathematical Physics, and we will create a very simple explanation and pack it all in a very visual and easy to digest video. Please, let us know in the comments what kind of content you want us to post about (related to Math & Mathematical Physics) so that we can help you! Contact us at: [email protected] Or visit our website: dibeos.net

Video Description

Operator theory is one of the foundations of Quantum Mechanics and it’s one of those mathematical areas that stores the craziest things that can possibly happen in what we call reality. And the theorem we will talk about today, is a way of shedding light into the dark universe of Hilbert spaces. This is the most powerful theorem in Operator Theory, called the Spectral Theorem.  PDF link if you want a more detailed explanation: https://dibeos.net/2025/12/20/the-most-powerful-theorem-in-operator-theory/ Full PDF with a more complete explanation and exercises can be found here: https://di-beos-shop.fourthwall.com/products/spectral-theorem Functional Analysis by Walter Rudin https://amzn.to/495sHEn --- Become a member to support us. Those who sign up for the 'Members' tier get Full PDFs for free. We appreciate your support! https://www.youtube.com/channel/UC3Z1rXCFFadHw69-PZpQRYQ/join Visit our site to sign up with your email: https://dibeos.net --- Our goal is to be the #1 math channel in the world. Please, give us your feedback, and help us achieve this ambitious dream. --- Some great books for learning math or physics https://www.amazon.com/hz/wishlist/ls/OUBVJVG21N5W?ref_=wl_share 🥹 Consider supporting us on Patreon: https://www.patreon.com/user?u=86646021

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