Day 232: Normed Spaces and Banach Spaces

Learning Objectives

• •**Define** a norm and verify the norm axioms for given examples
• •**Explain** why normed spaces generalize the concept of length to infinite dimensions
• •**Prove** that every normed space is a metric space
• •**Define** Banach spaces and explain the significance of completeness
• •**Work with** the $$\ell^p$$ sequence spaces, especially $$\ell^1$$, $$\ell^2$$, and $$\ell^\infty$$
• •**Connect** normed spaces to the structure of quantum state spaces

Today's Schedule (7 hours)