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Vector
semi-inner products
Kyle Rose, Christopher Schwanke and Zachary Ward
Vol. 15 (2022), No. 2, 289–297
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Abstract |
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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 whose codomain is a geometric mean closed vector lattice. 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
vector lattice, semi-inner product, Pythagorean theorem,
parallelogram law
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Mathematical Subject Classification
Primary: 46A40
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Milestones
Received: 29 April 2021
Revised: 21 September 2021
Accepted: 20 October 2021
Published: 29 July 2022
Communicated by Mohammad Sal Moslehian
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Authors |
| Kyle Rose | |
| Department of Mathematics Lyon College Batesville, AR United States |
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| Christopher Schwanke | |
| Department of Mathematics and
Applied Mathematics Hatfield Campus University of Pretoria Pretoria South Africa |
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| Zachary Ward | |
| Department of Mathematics Lyon College Batesville, AR United States |
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