Theory of Bounded Operators on Hilbert Space

This lecture covers the theory of bounded operators on Hilbert space, including adjoint and basic properties, self-adjointness, isometries, and unitaries. Examples such as left- and right-shift operators on ℓ² are discussed, along with definitions for unbounded operators, extensions, symmetric operators, adjoints, and self-adjoint operators. The lecture also explores momentum on the interval and the concept that generators of translation groups are self-adjoint.