Indefinite Halmos, Egervary and Sz.-Nagy Dilations

TL;DR

This paper proves that all self-adjoint operators on indefinite inner product modules over a characteristic 2 *-ring can be dilated using classical methods like Halmos, Egervary, and Sz.-Nagy dilations.

Contribution

It extends the theory of operator dilations to indefinite inner product modules over characteristic 2 *-rings, a novel setting.

Findings

Every self-adjoint operator admits classical dilations.

Extension of dilation theory to indefinite modules.

Applicable to modules over characteristic 2 *-rings.

Abstract

Let $\mathcal{M}$ be an indefinite inner product module over a *-ring of characteristic 2. We show that every self-adjoint operator on $\mathcal{M}$ admits Halmos, Egervary and Sz.-Nagy dilations.