|
In operator theory, the commutant lifting theorem, due to Sz.-Nagy and Foias, is a powerful theorem used to prove several interpolation results. ==Statement== The commutant lifting theorem states that if ''T'' is a contraction on a Hilbert space ''H'', ''U'' is its minimal unitary dilation acting on some Hilbert space ''K'' (which can be shown to exist by Sz.-Nagy's dilation theorem), and ''R'' is an operator on ''H'' commuting with ''T'', then there is an operator ''S'' on ''K'' commuting with ''U'' such that : and : 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''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「commutant lifting theorem」の詳細全文を読む スポンサード リンク
|