Functional Model of Commutative Operator Systems

Анотація

A functional model for a commutative system of the linear bounded operators $\{T_1, T_2\}$, when $T_1$ is a contraction, is built. The construction of functional model is based on an analogue with many parameters of the Lax - Phillips scattering scheme for the isometric dilation $U(n)$ of the semigroup with two parameters $T(n)=T_1^{n_1}T_{2}^{n_2}$ , where $n=(n_1,n_2)\in \mathbb{Z}^2_{+}$.

Mathematics Subject Classification: 47A45.