Day 244: Compact Operators

Learning Objectives

• •**Define** compact operators and explain their significance
• •**Characterize** compact operators as limits of finite-rank operators
• •**Prove** basic properties: compactness preserved under limits, products, adjoints
• •**Work with** Hilbert-Schmidt operators and their inner product structure
• •**Introduce** trace class operators and the trace functional
• •**Connect** compact operators to quantum mechanics (density matrices, Green's functions)

Today's Schedule (7 hours)