Families of Annihilating Skew-Selfadjoint Operators and their Connection to Hilbert Complexes

TL;DR

This paper explores the relationship between Hilbert complexes and annihilating sets of skew-selfadjoint operators, offering a new perspective on classical operator theory by connecting these concepts.

Contribution

It introduces the concept of annihilating sets of skew-selfadjoint operators and links them to Hilbert complexes, providing a novel viewpoint on their structure and properties.

Findings

Hilbert complexes are strongly related to annihilating sets of skew-selfadjoint operators

Provides a new perspective on classical Hilbert complex theory

Connects families of commuting normal operators to annihilating sets

Abstract

In this short note we show that Hilbert complexes are strongly related to what we shall call annihilating sets of skew-selfadjoint operators. This provides for a new perspective on the classical topic of Hilbert complexes viewed as families of commuting normal operators.