In this thesis we address two problems from the fields of operator algebras and operator theory. In our first problem, we seek to obtain a description of the unital subalgebras $\mathcal{A}$ of $\mathbb{M}_n(\mathbb{C})$ ...

We may associate to a C*-algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ...