## Hölder and Young inequalities for the trace of operators

• Manjegani S
• 6

• 16

Citations

#### 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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