Compact Linear Operator

Overview


Given two normed spaces (space equipped with a norm) {% X %} and {% Y %}, a linear operator
{% T: X \rightarrow Y %}
is compact if given any bounded sequence {% {x_1, x_2...} %} in {% X %}, the sequence that results from applying {% T %} ({% {Tx_1, Tx_2,...} %}) has a convergent subsequence.

Topics


  • Spectral Theorem of Compact Self-Adjoint Operators