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A remark on the non commutative Hölder inequality. (Une remarque sur l’inégalité de Hölder non commutative.) (French) Zbl 0784.46046

Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 595 (1992).
[For the entire collection see Zbl 0754.00008.]
A simple proof of Hölder’s inequality in a finite von Neumann algebra is given, with a special emphasis on the case of equality. The main tool is the joint distribution of a pair of self-adjoint operators affiliated with the algebra.

MSC:

46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras

Citations:

Zbl 0754.00008