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 State extensions of states on $\text{UHF}_n$ algebra to Cuntz algebra Bull. Korean Math. Soc. 2002 Vol. 39, No. 3, 471-478 Printed September 1, 2002 Dong-Yun Shin University of Seoul Abstract : Let $\eta = \{\eta_m \}_m$ be an eventually constant sequence of unit vectors $\eta_m$ in $\Bbb C^n$ and let $\rho_\eta$ be the pure state on $\text{UHF}_n$ algebra which is defined by $\rho_{\eta} (v_{i_1} \cdots v_{i_k} v_{j_k}^* \cdots v_{j_1}^* )= \overline{\eta_1^{i_1}\cdots \eta_k^{i_k}} \eta_k^{j_k} \cdots \eta_1^{j_1}.$ We find infinitely many state extensions of $\rho_{\eta}$ to Cuntz algebra $\Cal O_n$ using representations and unitary operators. Also, we present their concrete expressions. Keywords : Cuntz algebra, $\text{UHF}_n$ algebra, state, extension MSC numbers : Primary 46L30; Secondary 46L35 Downloads: Full-text PDF