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 Tr. Mat. Inst. Steklova, Forthcoming paper (Mi tm4072)

Schatten class operators in a representation space of Canonical Commutation Relations

A. S. Holevo

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Schatten classes $\mathfrak{S}_{p}$ of operators in a Hilbert space – the 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.

UDC: 519.248.3
Revised: October 14, 2019
Accepted: January 27, 2020