Extremal Positive Semidefinite Forms.
Extreme Points of a Convex Subset of the Cone of Positive Semidefinite Matrices.
Extreme points of the complex binary trilinear ball
We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
Extreme preservers of maximal column rank inequalities of matrix sums over semirings
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.