Functional Analysis I: Closed Operators

This lecture covers the concept of closed operators in functional analysis, focusing on Banach spaces X and Y. It discusses the verification of closed operators, the graph of an operator, and the definition of a closed operator. The lecture also explores the properties of closed operators in Banach spaces, such as completeness and boundedness. Additionally, it delves into the theorem of bounded inverses and the concept of direct sum of spaces. The corollary emphasizes the boundedness of projections in the context of closed operators.