Hu, Yao-Zhong 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. Reviewer: S.Goldstein (Łódź) MSC: 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras Keywords:non-commutative Hölder inequality; trace; Hölder’s inequality in a finite von Neumann algebra; joint distribution of a pair of self-adjoint operators affiliated with the algebra Citations:Zbl 0754.00008 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML