蓝子堡公式之推广及Буняковский不等式之再推广

<正> 本文系继前一文而作,本文中的主要结果为推广蓝子堡的公式

A GENERALIZATION OF A FORMULA OF LANDSBERG AND A FURTHER GENERALIZATION OF AN INEQUALITY OF BUNIAKOWSKY

The main purpose of this paper is to prove the following formula(?)(1)and the following two inequalities(?)(2)(?)(3)where m, n_1,n_2,…,n_m denote arbitrary finite positive integers n_0=1,(?)a_(ij)denotes the determinant of the n-th order of which the element in the i-throw and the j-th column is a_(ij) and(?)In(3)and(4),α_(s_1s_2)…s_m,and β_(t_1t_2)…t_m denote elements of an arbitraryHilbert space(complete or non-comptete,separable or non-separable),(α,β)denotes the inner product of the two elements α andβof this Hilbertspace.