Journal of the Ramanujan Mathematical Society

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Quantum Entropy Theoretic Aspects of the 13th Problem Formulated by Hilbert


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1 Department of Mathematics, Niigata University 8050, 2-Nomachi, Igarashi Niigata-Shi, 950-21, Japan
     

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The degree of continuity of normal states related to the quasi σ -strong operator topologies is characterized by the quantum entropy theoretic dimension. This result is applied to the study of Baire's category theoretic structure of the normal state space and the representability problem of normal states on tensor product operator algebras, which is based on the 13th Problem formulated by Hilbert.
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  • Quantum Entropy Theoretic Aspects of the 13th Problem Formulated by Hilbert

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Authors

Shigeo Akashi
Department of Mathematics, Niigata University 8050, 2-Nomachi, Igarashi Niigata-Shi, 950-21, Japan

Abstract


The degree of continuity of normal states related to the quasi σ -strong operator topologies is characterized by the quantum entropy theoretic dimension. This result is applied to the study of Baire's category theoretic structure of the normal state space and the representability problem of normal states on tensor product operator algebras, which is based on the 13th Problem formulated by Hilbert.