This course studies the central ideas of functional analysis, focussing primarily on normed vector spaces.

Highlights include:

• The Hahn-Banach theorem (in various guises)
• The open mapping and closed graph theorems
• The Banach-Steinhaus theorem
• Dual spaces
• Weak convergence
• Banach-Alaoglus theorem
• Spectral theory for self-adjoint operators

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