On isometric dilations of commutative systems of linear operators - Zolotarev, V. A. (Журнал математичної фізики, аналізу, геометрії, 2005)
The isometric dilation of two parameter semigroup T(n)=T^n_1_1 T^n_2_2, where n=(n_1,n_2)Z^2_+, for a commutative system {T_1,T_2} of linear bounded operators, one of which is a contraction, ||T_1||1, is constructed. The building of the dilation is based on characteristic qualities of the commutative isometric expansion {V_s,+V_s}_s=1^2, which was given in the previous work by the author [8]. The isometric dilations U(n) and +U\!\!(n) of the semigroups T(n) and T^*(n) are shown to be unitarily linked. Mathematical Subject Classification: 47A45.