Inner product spaces and Krein spaces in the quaternionic setting

TL;DR

This paper explores quaternionic inner product and Krein spaces, demonstrating that uniformly positive subspaces are ortho-complemented, with results on decompositions and topological properties.

Contribution

It establishes that uniformly positive subspaces in quaternionic Krein spaces are ortho-complemented, advancing the understanding of their structure and topological features.

Findings

Uniformly positive subspaces are ortho-complemented in quaternionic Krein spaces

Results on fundamental decompositions of quaternionic inner product spaces

Topological properties of quaternionic Krein spaces

Abstract

In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.