Functional Analysis

  1. Linear Operators on Normed Spaces
    1. Basic Definitions
      1. Linear Operators
        1. Domain and Range
          1. Graph of an Operator
            1. Examples of Linear Operators
            2. Boundedness and Continuity
              1. Bounded Linear Operators
                1. Equivalence of Boundedness and Continuity
                  1. Operator Norm
                    1. Examples and Calculations
                    2. Space of Bounded Linear Operators
                      1. B(X,Y) as Normed Space
                        1. Completeness of B(X,Y)
                          1. Algebraic Operations
                            1. Composition of Operators
                            2. Special Types of Operators
                              1. Linear Functionals
                                1. Isomorphisms
                                  1. Isometries
                                    1. Projections
                                      1. Compact Operators
                                      2. Kernel and Range
                                        1. Null Space Properties
                                          1. Range Properties
                                            1. Rank and Nullity
                                              1. Closed Range Theorem

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                                            4. Hilbert Spaces

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                                            6. Fundamental Theorems of Functional Analysis