On $(a,b,c,d)$-orthogonality in normed linear spaces
Volume 103 / 2005
Colloquium Mathematicum 103 (2005), 1-10
MSC: Primary 46C05, 46C10.
DOI: 10.4064/cm103-1-1
Abstract
We first introduce a notion of $(a,b,c,d)$-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known $\alpha $- and $(\alpha ,\beta )$-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.
