Hilbert Space and Midpoint Convex Set with Reference to Projection and Trijection
Abstract: In this paper, we explore the geometric structural properties of a specialized subset within a Hilbert space defined via the inner product and the set of dyadic rational numbers. For a fixed element, we define the set. We demonstrate three key topological and algebraic results: first, that constitutes a midpoint convex set of; second, that for any two subsets and of such that, the containment relation holds strictly; and third, that the operator set of is invariant under its dyadic convex hull, satisfying, where represents the midpoint convex hull of. These findings provide fresh structural insights into sequence-to-set maps within inner product spaces.
Keywords: Hilbert space, Midpoint convexity, Dyadic rational numbers, Inner product spaces, Dyadic convex hull
How to Cite?: Dr. Haresh Gambhir Chaudhari, "Hilbert Space and Midpoint Convex Set with Reference to Projection and Trijection", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 20-21, https://www.ijsr.net/getabstract.php?paperid=SR26627115925, DOI: https://dx.doi.org/10.21275/SR26627115925