Noncommutative Analysis

Tag: Krein-Milman theorem

Advanced Analysis, Notes 14: Banach spaces (application: the Stone–Weierstrass Theorem revisited; structure of C(K))

In this post we will use the Krein–Milman theorem together with the Hahn–Banach theorem to give another proof of the Stone–Weierstrass theorem. The proof we present does not make use of the classical Weierstrass approximation theorem, so we will have here an alternative proof of the classical theorem as well.

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Advanced Analysis, Notes 13: Banach spaces (convex hulls and the Krein–Milman theorem)

It would be strange to disappear for a week without explanations. This blog was not working for the past week because of the situation in Israel. The dedication in the beginning of the previous post had something to do with this, too. We are now back to work, with the modest hope that things will remain quiet until the end of the semester. We begin our last chapter in basic functional analysis, convexity and the Krein–Milman theorem.

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