Vector semi-inner products
Functional Analysis
2021-09-23 v2
Abstract
We formalize the notion of vector semi-inner products and introduce a class of vector seminorms which are built from these maps. The classical Pythagorean theorem and parallelogram law are then generalized to vector seminorms that have a geometric mean closed vector lattice for codomain. In the special case that this codomain is a square root closed, semiprime -algebra, we provide a sharpening of the triangle inequality as well as a condition for equality.
Keywords
Cite
@article{arxiv.2104.14484,
title = {Vector semi-inner products},
author = {Kyle Rose and Christopher Schwanke and Zachary Ward},
journal= {arXiv preprint arXiv:2104.14484},
year = {2021}
}