Speaker
Description
We consider general bilinear products parameterized by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower bound in the Loewner order, generalizing previous results of Vybíral and Khare that were obtained in the special case of the Hadamard product. Our results naturally extend to Hilbert spaces for a family of products parametrized by positive trace-class operators, providing a lower bound in the Loewner order for such general products, including for the Hilbert tensor product.
(Joint work with Javad Mashreghi and Prateek Kumar Vishwakarma.)