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
 * /3 - $A : X \to Y$ is compact iff for every bounded sequence $\sequence {x_n}$, there exists a subsequence $\sequence {x_{n_j}}$ such that $\sequence {A x_{n_j}}$ converges.
 * /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