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arXiv · 2104.14484

Vector semi-inner products

Kyle Rose·Christopher Schwanke·Zachary Ward
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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 $f$-algebra, we provide a sharpening of the triangle inequality as well as a condition for equality.

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Kyle Rose, Christopher Schwanke, Zachary Ward. 2021-04-29. Vector semi-inner products. https://arxiv.org/abs/2104.14484

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