Banach-Steinhaus Theorem

This lecture covers the Banach-Steinhaus and closed graph theorems, focusing on the study of unbounded operators and the search for domains where an operator is self-adjoint. The presentation includes technical results and a lemma for normed spaces. The Banach-Steinhaus theorem is discussed in detail, emphasizing the concept of uniform boundedness and providing a proof by contradiction. The lecture concludes with the convergence of a Cauchy sequence and the implications for operator norms.