2021/04/29 by Kyle Rose, Rose, Kyle, Christopher Schwanke +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2104.14484
openalex publication_date 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.