commutant lifting theorem

English

commutant lifting theorem

(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 ${\\displaystyle RT^{n}=P_{H}SU^{n}\\vert _{H}\\;\\forall n\\geq 0,}$ and ${\\displaystyle \\Vert S\\Vert =\\Vert R\\Vert }$ . 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.

单词	commutant lifting theorem
释义	commutant lifting theorem English Proper noun commutant lifting theorem (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 ${\\displaystyle RT^{n}=P_{H}SU^{n}\\vert _{H}\\;\\forall n\\geq 0,}$ and ${\\displaystyle \\Vert S\\Vert =\\Vert R\\Vert }$ . 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.
随便看	ridacchiavano ridacchiavate ridacchiavi ridacchiavo ridacchierai ridacchieranno ridacchierebbe ridacchierebbero ridacchierei ridacchieremmo ridacchieremo ridacchiereste ridacchieresti ridacchierete ridacchierà ridacchierò ridacchino ridacchio ridacchiò ridado ridadoj ridadojn ridadon ridaesero ridaforolimus