Rad HAZU, Matematičke znanosti, Vol. 19 (2015), 13-26.

ORTHOGONAL PROJECTION OF AN INFINITE ROUND CONE IN REAL HILBERT SPACE

Mate Kosor

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.

2010 Mathematics Subject Classification.   15A63, 46C05, 26D15, 51M05, 51M04.

Key words and phrases.   Round cone, aperture, projection, angle, reverse Cauchy inequality.

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