Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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STATE EXTENSIONS OF STATES ON UHFn ALGEBRA TO CUNTZ ALGEBRA

  • Published : 2002.08.01
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Abstract

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.

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References

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  1. Classification of Sub-Cuntz States vol.18, pp.2, 2015, https://doi.org/10.1007/s10468-014-9509-4
  2. Pure States on Cuntz Algebras Arising from Geometric Progressions vol.19, pp.6, 2016, https://doi.org/10.1007/s10468-016-9619-2