# A distance formula related to a family of projections orthogonal to their symmetries

## TL;DR

This paper derives an exact formula for the distance between a projection and a specific set of projections related to a hermitian involution in a Hilbert space, expanding understanding of projection distances in operator algebras.

## Contribution

It introduces a precise distance formula involving the norm of eue for projections orthogonal to symmetries, within the algebra generated by e and u.

## Key findings

- Derived an exact formula for the projection distance
- Connected the distance to the norm of eue
- Enhanced understanding of projection relations in operator algebras

## Abstract

Let u be a hermitian involution, and e an orthogonal projection, acting on the same Hilbert space. We establish the exact formula, in terms of the norm of eue, for the distance from e to the set of all orthogonal projections q from the algebra generated by e,u, and such that quq=0.