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

Massive refactor
Loads of definitions are specifically for Hilbert spaces, will mostly be split off into definitions for normed vector spaces and inner product spaces. The latter basically being the former but defining the inner product norm and using that. This is mainly causing a problem because the spectral theory stuff seems to be down between general normed vector spaces.


 * /Definition:Bounded Linear Transformation
 * /Definition:Bounded Linear Operator
 * /Definition:Eigenvalue
 * /Definition:Inverse (Bounded Linear Transformation)
 * /Definition:Norm/Bounded Linear Transformation
 * /Definition:Space of Bounded Linear Transformations