# A note on alternating projections in Hilbert space

## TL;DR

This paper offers a direct proof of the asymptotic behavior of alternating projections onto convex sets in Hilbert space, utilizing nonexpansive mapping theory to clarify convergence properties.

## Contribution

It presents a new, direct proof of the asymptotic behavior of alternating projections in Hilbert spaces, enhancing understanding with a nonexpansive mapping approach.

## Key findings

- Proof of asymptotic convergence of alternating projections
- Application of nonexpansive mapping theory to projection analysis
- Clarification of convergence behavior in Hilbert spaces

## Abstract

We provide a direct proof of a result regarding the asymptotic behavior of alternating nearest point projections onto two closed and convex sets in a Hilbert space. Our arguments are based on nonexpansive mapping theory.