Mathematische Annalen

, Volume 325, Issue 4, pp 727–744 | Cite as

Young's inequality in trace-class operators

  • Martín Argerami
  • Douglas R. Farenick


 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.


Trace Class Partial Isometry Young Inequality Schmidt Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Martín Argerami
    • 1
  • Douglas R. Farenick
    • 2
  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 172 (1900) La Plata, Argentina (e-mail:
  2. 2.Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada (e-mail:

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