Generalizations of Dobrushin's inequalities and applications

[摘要] Let f: R(n) --> R be a seminorm and let (e(i))(1 less than or equal to i less than or equal to n) be the canonical base of R(n). Denote M = 1/2 max(r,s)f(e(r) - e(s)), K = max(r)f(e(r)). We prove the inequality f(x) less than or equal to M ((i = 1)Sigma(n)\x(i)\ + (K - M) \(i = 1)Sigma(n)x(i)\, x = (x(1), x(2),..., x(n)) is an element of R(n). We use the above inequality to prove some generalizations of Dobrushin's inequalities and a generalization of an inequality due to J. E. Cohen et al. (Linear Algebra Appl. 179, 1993, 211-235). Hilbert space generalizations of the above inequalities are proved using Levi's reduction theorem. As special cases of our results we obtain several inequalities given previously by Adamovici, Djokovic, Hlawka, and Hornich. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-15