Compact operator on Hilbert space
hypernym: Extension
name: Lemma
subject: Category:Linear operators
subject: Category:Hilbert spaces
math statement: If H a finite-dimensional Hilbert space, and a commutative set of operators, each of which is diagonalisable; then the operators can be simultaneously diagonalized.
math statement: Suppose all the operators in are compact. Then every closed non-zero -invariant sub-space has a common eigenvector for .
name: Theorem 1
description: functional analysis concept
subject: Category:Articles containing proofs
name: Theorem 3
label: Συμπαγής τελεστής σε χώρο Hilbert @el
math statement: If all the operators in are compact then the operators can be simultaneously diagonalized.
name: Theorem 2
math statement: If there is an injective compact operator in ; then the operators can be simultaneously diagonalized.
label: ヒルベルト空間上のコンパクト作用素 @ja
subject: Category:Operator theory