"commutant lifting theorem" meaning in English

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      "glosses": [
        "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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      "raw_glosses": [
        "(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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        "mathematics",
        "sciences"
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      "wikipedia": [
        "commutant lifting theorem"
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  "word": "commutant lifting theorem"
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        "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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        "(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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