User:Caliburn/s/fa
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Spectral Theory
- /Definition:Resolvent Set of Linear Operator
- /Definition:Resolvent of Linear Operator
- /Definition:Spectrum of Linear Operator
- /Resolvent Set of Linear Operator is Open
- /Spectrum of Linear Operator is Closed
- /Spectrum of Linear Operator is Bounded
- /1 - $\lambda \in \map \sigma A$ iff $\overline \lambda \in \map \sigma {A^*}$
- /2
- /Space of Compact Linear Transformations is Linear Subspace of Space of Bounded Linear Transformations
- /Space of Compact Linear Transformations is Closed in Space of Bounded Linear Transformations
- /Compact Hermitian Operator has Eigenvalue
- /Eigenspace Corresponding to Non-Zero Eigenvalue of Compact Operator is Finite Dimensional
- /Spectral Theorem for Compact Hermitian Operators
- /Spectrum of Linear Operator is Topological Closure of Point Spectrum
Separability
- /Topological Space containing Uncountable Family of Disjoint Open Subsets is not Separable
- /Subspace of Separable Metric Space is Separable
- /Characterization of Separable Normed Vector Space
- /p-Sequence Space is Separable
- /Normed Vector Space with Separable Dual is Separable
Dual Spaces
- /Dual of 1-Sequence Space Isometrically Isomorphic to Space of Bounded Sequences
- /Dual of p-Sequence Space
Hahn-Banach Theorem
- /Normed Vector Space with Separable Dual is Separable
- /Banach Limit Bounded Between Limit Inferior and Limit Superior
- /Existence of Banach Limit
- /Definition:Almost Convergent Sequence
Geometric Hahn-Banach
- /Hahn-Banach Separation Theorem/Open Convex Set and Convex Set
- /Hahn-Banach Separation Theorem/Compact Convex Set and Closed Convex Set
- /Closed Convex Set in terms of Bounded Linear Functionals
- /Convex Hull is Smallest Convex Set containing Set
Krein-Milman Theorem
Locally Convex Spaces
- /Definition:Locally Convex Space
- /Locally Convex Space is Hausdorff iff induces Hausdorff Topology
- /Locally Convex Space Induces Topology
- /Vector Addition in Locally Convex Space is Continuous
- /Scalar Multiplication in Locally Convex Space is Continuous
- /Hausdorff Locally Convex Space is Topological Vector Space
- /Characterization of Convergence in Locally Convex Space
- /Definition:Fréchet Space
- /Normed Vector Space is Locally Convex Space
- /Characterization of Continuous Linear Transformations between Locally Convex Spaces
General Stuff about TVSs
- /Definition:Translation Operator on Topological Vector Space
- /Definition:Multiplication Operator on Topological Vector Space
- /Translation Operator on Topological Vector Space is Homeomorphism
- /Multiplication Operator on Topological Vector Space is Homeomorphism
- /Translation of Open Set in Topological Vector Space is Open
- /Dilation of Open Set in Topological Vector Space is Open
- /Definition:Bounded Subset of Topological Vector Space
- /Definition:Locally Bounded Topological Vector Space
- /Definition:Locally Compact Topological Vector Space
- /Definition:F-Space
- /Definition:Fréchet Space
Massive refactor
- /Definition:Diagonalizable Operator
- /Definition:Finite Rank Operator
- /Definition:Space of Continuous Finite Rank Operators
- /Definition:Space of Compact Linear Transformations
- /Definition:Compact Linear Transformation
- /Definition:Real Part (Linear Operator)
- /Definition:Bounded Sesquilinear Form
- /Definition:Imaginary Part (Linear Operator)
- /Definition:Inverse (Bounded Linear Transformation)
- /Definition:Norm/Bounded Linear Transformation
- /Definition:Space of Bounded Linear Transformations