Welcome to my Honors Thesis landing page.

Paradoxical Decompositions and Tarski’s Theorem

The focus here is on the Banach–Tarski paradox and Tarski’s theorem.

Functional Analysis: Topological Vector Spaces

Here, I work through a lot of first four chapters of my professor’s textbook in functional analysis.

Invariant States and Means on Groups

I work through some results related to free groups, means, invariant states, and growth rates.

Functional Analysis: Hilbert Spaces

I work through chapters 5 and 6 of my professor’s functional analysis textbook, focused on the structure of Hilbert spaces and the algebra of bounded operators on a Hilbert space.

Functional Analysis: Banach and C*-Algebras

We generalize from the bounded operators on a Hilbert space to discuss Banach algebras and C*-algebras, the latter of which admit representations as bounded operators on Hilbert spaces via the GNS construction.

More on C*-Algebras

Notes for the final part of the thesis, on the left-regular representation, Kesten’s criterion, Hulanicki’s criterion, and properties of the group C*-Algebras.

Thesis Presentation

Final Thesis