Pfaffians, Hafnians and products of real linear functionals. (English) Zbl 1160.46311
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 Révész 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).
MSC:
46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
15A15 | Determinants, permanents, traces, other special matrix functions |
47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
60E15 | Inequalities; stochastic orderings |