Orthogonal Frames in Krein Spaces

In this paper, we introduce the concept of orthogonal frames in Krein spaces, prove the independence of the choice of the fundamental symmetry, and from this, we obtain a number of interesting properties that they satisfy. We show that there is no distinction between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert. Furthermore, we characterize frames dual to a given frame, which is a useful tool for constructing examples.

Automated summary

This paper introduces the concept and properties of orthogonal frames in Krein spaces. It proves the independence of the choice of the fundamental symmetry and derives interesting properties from it. Additionally, it demonstrates the equivalence between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert space. The paper also characterizes dual frames to a given frame, which is a useful tool for constructing examples.