Pfaffians, hafnians and products of real linear functionals

• Autores: Péter E. Frenkel
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 351-358
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n2.a12
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• Resumen

  • 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).