Spectrally additive maps on the positive cones of the Wiener algebra

TL;DR

This paper characterizes spectrum-preserving maps on the positive cones of the Wiener algebra, showing they extend to isometric linear isomorphisms, thus revealing structural rigidity of such transformations.

Contribution

It establishes that spectrum-preserving maps on the positive cones of the Wiener algebra extend to isometric linear isomorphisms, providing a new structural insight.

Findings

Spectrum-preserving maps extend to isometric linear isomorphisms.

The maps are surjective and preserve the spectrum of sums.

Structural rigidity of spectrum-preserving transformations in Wiener algebra.

Abstract

We study surjective maps between the positive cones of the Wiener algebra that preserve the spectrum of the sum of every two elements. We show that such maps can be extended to isometric real-linear isomorphisms of the Wiener algebra.