Michael Müger

### Operator Algebras (supplements to Murphy's book)

1) The Beurling-Garling formula for norm and spectral radius in a Banach algebra: `Elementary' proof without complex analysis.
(pdf file)

2) On M(A)
(pdf file)

3) On trace class operators (and Hilbert-Schmidt operators)
(pdf file)

4) Pure states and the irreducibility of GNS representations
(pdf file)

5) On monotone complete C*-algebras and a characterization of von Neumann algebras
(pdf file)

### Other matters

1) A remark on the invariance of dimension. (Published)
(arXiv:1310.8090)
(pdf file)

2) The prime number theorem via Karamata's proof of Ingham's tauberian theorem.
(arXiv:1311.2491)
(close to published version)

(Improved version)

3) (Almost) Real Proof of the Prime Number Theorem.
(pdf file)

4) The Prime Number Theorem without Euler products
(pdf file)

5) The Mean Value Inequality.
(pdf file)

6) Notes on the theorem of Baker-Campbell-Hausdorff-Dynkin (Work in progress!)
(pdf file)

7) Some Fourier series (well-known constructions, written up with minimal overhead, of continuous periodic functions with Fourier series that are (a) not-absolutely convergent, (b) divergent at a point.)
(pdf file)