Abstract. We introduce the notion of $Q$-commuting operators which includes commuting operators. We prove a generalized version of the commutant lifting theorem and Ando's dilation theorem in the context of $Q$-commuting operators.

DOI: 10.14232/actasm-019-775-2

AMS Subject Classification (1991): 47A20

Keyword(s): isometric dilation, unitary dilation, co-isometric extension, commutant lifting, Ando's dilation theorem

received 25.5.2019, revised 21.10.2019, accepted 28.10.2019. (Registered under 525/2019.)