泛函分析

Functional Analysis · Interactive

From normed spaces and Banach spaces to spectral theory and operator algebras. A rigorous journey through infinite-dimensional analysis with interactive visualizations.

Course Roadmap

Part A: Foundations

  • Ch 0: Metric Spaces & Topological Preliminaries
  • Ch 1: Normed Spaces
  • Ch 2: Banach Spaces
  • Ch 3: Inner Product Spaces & Hilbert Spaces
  • Ch 4: Orthogonality & Projections

Part B: The Big Theorems

  • Ch 5: Bounded Linear Operators
  • Ch 6: Hahn–Banach Theorem
  • Ch 7: Baire Category Theorem
  • Ch 8: Uniform Boundedness Principle
  • Ch 9: Open Mapping & Closed Graph

Part C: Duality & Weak Topologies

  • Ch 10: Dual Spaces
  • Ch 11: Weak & Weak* Topologies
  • Ch 12: Reflexive Spaces
  • Ch 13: Lp Spaces

Part D: Spectral Theory

  • Ch 14: Compact Operators
  • Ch 15: Fredholm Theory
  • Ch 16: Spectral Theory for Compact Operators
  • Ch 17: Banach Algebras & Gelfand Theory

Part E: Advanced Topics

  • Ch 18: Unbounded Operators
  • Ch 19: Distributions & Sobolev Spaces

Select a chapter from the sidebar to begin.