Definitions from Wiktionary (commutant lifting theorem)
▸ noun: (mathematics) A theorem in operator theory, stating that, if T is a contraction on a Hilbert space H, and U is its minimal unitary dilation acting on some Hilbert space K, and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that RTⁿ=P_HSUⁿ|_H;∀n≥0, and ‖S‖=‖R‖. In other words, an operator from the commutant of T can be "lifted" to an operator in the commutant of the unitary dilation of T.
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▸ noun: (mathematics) A theorem in operator theory, stating that, if T is a contraction on a Hilbert space H, and U is its minimal unitary dilation acting on some Hilbert space K, and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that RTⁿ=P_HSUⁿ|_H;∀n≥0, and ‖S‖=‖R‖. In other words, an operator from the commutant of T can be "lifted" to an operator in the commutant of the unitary dilation of T.
Similar:
von Neumann's inequality,
commutator,
commutant,
multicommutator,
lifting,
hyperoperator,
commutator length,
superoperator,
linear operator,
Hermitian conjugate,
more...
▸ Words similar to commutant lifting theorem
▸ Usage examples for commutant lifting theorem
▸ Idioms related to commutant lifting theorem
▸ Wikipedia articles (New!)
▸ Words that often appear near commutant lifting theorem
▸ Rhymes of commutant lifting theorem
▸ Invented words related to commutant lifting theorem