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Young's inequality in trace-class operators

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Abstract.

 If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥1 denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 172 (1900) La Plata, Argentina (e-mail: martin@mate.unlp.edu.ar), , , , , , AR

    Martín Argerami

  2. Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada (e-mail: farenick@math.uregina.ca), , , , , , CA

    Douglas R. Farenick

Authors
  1. Martín Argerami
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  2. Douglas R. Farenick
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Additional information

Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003

Mathematics Subject Classification (2000): 47A63, 15A60

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Argerami, M., Farenick, D. Young's inequality in trace-class operators. Math. Ann. 325, 727–744 (2003). https://doi.org/10.1007/s00208-002-0400-y

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  • DOI: https://doi.org/10.1007/s00208-002-0400-y

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