Vector semi-inner products
Copyright policy )Vector semi-inner products
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.
- University of Pretoria South Africa
- Lyon College United States
Mathematics - Functional Analysis, Parallelogram law, Vector lattice, semi-inner product, FOS: Mathematics, vector lattice, parallelogram law, Pythagorean theorem, Semi-inner product, Ordered topological linear spaces, vector lattices, Functional Analysis (math.FA)
Mathematics - Functional Analysis, Parallelogram law, Vector lattice, semi-inner product, FOS: Mathematics, vector lattice, parallelogram law, Pythagorean theorem, Semi-inner product, Ordered topological linear spaces, vector lattices, Functional Analysis (math.FA)
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