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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 309, Pages 165–173
DOI: https://doi.org/10.4213/tm4072 (Mi tm4072) 		 
Schatten Class Operators in a Representation Space of Canonical Commutation Relations

A. S. Holevo

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4072
Abstract: The Schatten classes $\mathfrak S_p$ of operators in a Hilbert space—a noncommutative analog of the classical $l_p$ spaces—play a significant role in recent studies on quantum information theory. In the present paper we give sufficient conditions for an operator to belong to $\mathfrak S_p$ in the case where the Hilbert space is the space of an irreducible representation of the canonical commutation relations.
Received: September 14, 2019
Revised: October 14, 2019
Accepted: January 27, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 309, Pages 150–158
DOI: https://doi.org/10.1134/S0081543820030116
Bibliographic databases:
Document Type: Article
UDC: 519.248.3
Language: Russian
Citation: A. S. Holevo, “Schatten Class Operators in a Representation Space of Canonical Commutation Relations”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 165–173; Proc. Steklov Inst. Math., 309 (2020), 150–158
Citation in format AMSBIB
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\pages 165--173
\publ Steklov Math. Inst. RAS
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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