Mathematical Research Letters

Volume 15, Issue 2, March 2008 pp. 351-358.

Pfaffians, hafnians and products of real linear functionals

Authors: Péter E. Frenkel
Author institution: Hungarian Academy of Sciences

Summary: We prove pfaffian and hafnian versions of Lieb's inequalities on determinants and permanents of positive semi-definite matrices. We use the hafnian inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the norm of a product of linear functionals on a real Euclidean space (this subject is sometimes called the `real linear polarization constant' problem).

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