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

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.

Key words and phrases: Hilbert complexes, de Rham complex, elasticity complex, biharmonic complex, factorisation of hyperbolic problems