STATE EXTENSIONS OF STATES ON UHFn ALGEBRA TO CUNTZ ALGEBRA

Let $Let\eta={\eta m}m$ be an eventually constant sequence of unit vectors $\eta m$ in $C^{n}$ and let $\rho$η be the pure state on $UHF_{n}$ algebra which is defined by $\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}$. We find infinitely many state extensions of $\rho\eta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.