• commutant lifting theorem

commutant lifting theorem (suomeksi)

Määritelmät:

• (lb, en, math) 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 $R\; T^n\; =\; P\_H\; S\; U^n\; \backslash vert\_H\; \backslash ;\; \backslash forall\; n\; \backslash geq\; 0,$ and $\backslash Vert\; S\; \backslash Vert\; =\; \backslash Vert\; R\; \backslash Vert$. 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''.