Some Inequalities in Pseudo-Hilbert Spaces

Loredana Ciurdariu

Tamkang Journal of Mathematics

42卷4期（2011 / 12 / 01）

483 - 492

英文

The aim of this paper is to obtain new versions of the reverse of the generalized triangle inequalities given in [4], and [5] if the pair (a(subscript i) ,x(subscript i)), i ∈ {1,...,n} from Theorem 1 of [4] belongs to C×H, where H is a Loynes Z-space instead of K×X, X being a normed linear space and K is the field of scalars. By comparison, in [4] the pair (a(subscript i) ,x(subscript i)), i ∈ {1,...,n} belongs to A^2, where A is a normed algebra over the real or complex number field K. The results will be given in Theorem 1, Theorem 3, Remark 2 and Corollary 3 which represent other interesting variants of Theorem 2.1, Remark 2.2, Theorem 3.2 and Theorem 3.4., see [4].