线性泛函在正定二次型下的范数

Norm of a Linear Functional for a Positive Definite Quadratic Form

设(V,‖.‖)是一个n维赋范空间,Q是V上的正定二次型,l是V上的单位线性泛函,当Q的单位球体积取极小值时,证明了:l的Q-范数‖l‖Q≤1,对某些特殊的li,‖li‖Q=1.

Let （ V, ‖·‖ ） be a normed vector space, Q be a positive definite quadratic form on V,and l be a unit linear functional on V. The author proves that if the volume of the unit ball of Q roaches minimum, then Q-norm of l, ‖ l ‖ Q ≤ 1, and ‖ li ‖ Q = 1 for some special unit linear functionals li ＇s.