Hölder and Young inequalities for the trace of operators

  • Manjegani S
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Abstract

If A1, . . . , Am are positive semidefinite n    n matrices, and if p1, . . . , pm are positive real numbers such that then




where |X| denotes and tr(X) denotes the trace of X. Moreover, equality holds in either of these inequalities if and only if . This result will be shown to hold as well in unital C*-algebras that have a faithful tracial state.

Author-supplied keywords

  • Hölder and Young inequalities
  • Singular values
  • Trace of operators

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Authors

  • Seyed Mahmoud Manjegani

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