On the model of a skew--selfadjoint operator with a simple spectrum on a Hilbert quaternion module

TL;DR

This paper develops a model for skew-selfadjoint operators with simple spectra on Hilbert quaternion modules, extending spectral theory to quaternionic settings.

Contribution

It constructs a spectral model for skew-selfadjoint operators on quaternionic Hilbert modules, based on the spectral theorem.

Findings

Established a spectral model for skew-selfadjoint operators on quaternionic Hilbert modules

Extended spectral theorem to quaternionic operator context

Provided foundational results for quaternionic operator theory

Abstract

In this work we construct the model of a skew--selfadjoint operator with a simple spectrum acting on a Hilbert quaternion bimodule. This result is based on the Spectral Theorem for a skew--selfadjoint operator.