Orthogonal Projection of an Infinite Round Cone in Real Hilbert Space

2014/02/07 by Mate Kosor, Kosor, Mate
Computer Science · Mathematics · #15A63 #26D15 #46C05 #51M04 #51M05 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications #Matrix Theory and Algorithms #math.FA #msc:15A63 #msc:26D15 #msc:46C05 #msc:51M04 #msc:51M05

paper · pdf · doi:10.48550/arxiv.1402.2952

openalex publication_date 2014/02/07 · arxiv created 2015/06/29 · arxiv updated 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between the orthogonal projections of the two vectors. The estimate depends on the angle between the two vectors and the position of only one of the two vectors. Our results also make a contributions to Cauchy-Bunyakovsky-Schwarz type inequalities.

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