Linear functionals on the Cuntz algebra期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Linear functionals on the Cuntz algebra

Authors:	Eui-Chai Jeong

Affiliation:	Department of Mathematics, Chung-Ang University, Dongjak-ku, Seoul, 156-756, South Korea

Abstract:	For a pure state on $mathcal{O}_n$ , which is an extension of a pure state on $mathrm{UHF}_n$ with the property that if $(mathcal{H}_{p'},pi_{p'},omega_{p'})$ is a corresponding representation, then $pi_{p'}(mathrm{UHF}_n)=B(mathcal{H}_{p'})$ , induces a unital shift of of the Powers index . We describe states on $mathrm{UHF}_n$ by using sequences of unit vectors in $mathbb{C} ^n$ . We study the linear functionals on the Cuntz algebra $mathcal{O}_n$ whose restrictions are the product pure state on $mathrm{UHF}_n$ . We find conditions on the sequence of unit vectors for which the corresponding linear functionals on $mathcal{O}_n$ become states under these conditions.

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