Absolute norms on Cn1

[摘要] In this paper, we study the absolute normalized norms on C-n. We show that the set of all absolute normalized norms on C-n is in one-to-one correspondence with the set Psi (n) of all continuous convex functions on Delta (n) with some suitable conditions, where Delta (n) = {(s(1),...,s(n-1)) is an element of Rn-1; s(1) + s(2) + ... + s(n-1) less than or equal to 1, s(i) greater than or equal to 0 (1 less than or equal to i less than or equal to n - 1)}. As some applications, we show that an absolute norm on C-n is strictly convex if and only if the corresponding function psi on Delta (n) is strictly convex. Further, we consider the von Neumann-Jordan constant of C-n with an absolute normalized norm. (C) 2000 Academic Press.

[发布日期] 2000-12-15