User:Caliburn/s/fa

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

 * /Extreme Set in Compact Convex Set contains Extreme Point
 * /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

so i don't lose these

 * Invertibility of Identity Minus Operator
 * Operator Norm on Banach Space is Submultiplicative