STATE EXTENSIONS OF STATES ON UHFn ALGEBRA TO CUNTZ ALGEBRA

Title & Authors
STATE EXTENSIONS OF STATES ON UHFn ALGEBRA TO CUNTZ ALGEBRA
Shin, Dong-Yun;

Abstract
Let $\small{Let\eta={\eta m}m}$ be an eventually constant sequence of unit vectors $\small{\eta m}$ in $\small{C^{n}}$ and let $\small{\rho}$η be the pure state on $\small{UHF_{n}}$ algebra which is defined by $\small{\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}}$. We find infinitely many state extensions of $\small{\rho\eta}$ to Cuntz algebra $\small{O_n}$ using representations and unitary operators. Also, we present theirconcrete expressions.
Keywords
Cuntz algebra;$\small{UHF_n}$ algebra;state;extension;
Language
English
Cited by
1.
Classification of Sub-Cuntz States, Algebras and Representation Theory, 2015, 18, 2, 555
2.
Pure States on Cuntz Algebras Arising from Geometric Progressions, Algebras and Representation Theory, 2016, 19, 6, 1297
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