Day 240: Operator Norm and B(H)

Learning Objectives

• •**Compute** operator norms using various characterizations
• •**Prove** that the operator norm satisfies the norm axioms
• •**Demonstrate** that $\mathcal{B}(\mathcal{H})$ is a Banach space (completeness)
• •**Explain** the Banach algebra structure and the submultiplicativity property
• •**Work with** the Neumann series and operator inverses
• •**Connect** the algebraic structure to quantum mechanical observables

Today's Schedule (7 hours)