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jxir's math pages
About
General Topology
Topological Spaces
Universal Constructions
Continuity & Convergence
Compactness
Tychonoff Product Theorem
Baire Spaces
Metric Spaces
Measure and Integration
Measure Theory
σ-Algebras
Measurable Maps
Borel Sets
Measures
Signed Measures
Lebesgue Integral
Almost Everywhere
Convergence Theorems
The L
p
Spaces
Complex Analysis
One Complex Variable
Basics
Power Series
Cauchy's Theorem
Cauchy's Integral Formula
Functional Analysis Basics
Normed Spaces
Dual Space, Adjoint Operator
The Fundamental Four
Hahn–Banach Theorem
Uniform Boundedness Theorem
Open Mapping Theorem
Closed Graph Theorem
Weak Convergence
Reflexive Spaces
Banach–Alaoglu Theorem
Inner Product Spaces
Orthogonality
Hilbert Spaces
More Functional Analysis
Topological Vector Spaces
Polar Topologies
Locally Convex Spaces
Alaoglu–Bourbaki Theorem
Krein–Milman Theorem
Operator Algebras
Banach Algebras
Operator Topologies
C*-Algebras
Positive Linear Functionals
States
Unbounded Operators
Hellinger–Toeplitz Theorem
Graph and Closedness
Functional Analysis Basics
Recommended Textbooks
Kreyszig, Erwin. 1978.
Introductory Functional Analysis With Applications
. John Wiley & Sons.
Table of contents
Normed Spaces
Dual Space, Adjoint Operator
The Fundamental Four
Weak Convergence
Reflexive Spaces
Banach–Alaoglu Theorem
Inner Product Spaces
Hilbert Spaces