Isometric Expansions of Quantum Algebra of Linear Bounded Operators

Анотація

The isometric expansion $\left\{V_s,\stackrel{+}{V_s}\right\}_{s=1}^2$ for a quantum algebra of linear bounded nonunitary operators $\{T_1,T_2\}$, which is given by commutative relation $T_1T_2=qT_2T_1$ $(|q|=1)$, is constructed. Basic properties of characteristic function $S(z)$ corresponding to isometric expansion $\left\{V_s,\stackrel{+}{V_s}\right\}_{s=1}^2$ for given quantum algebra $\{T_1,T_2\}$ are described.

Mathematics Subject Classification 2000: 47A45.