Frames on Krein Spaces

TL;DR

This paper extends the concept of frames from Hilbert spaces to Krein spaces, defining new notions and exploring their properties, including decomposition into orthonormal bases and relations with projections.

Contribution

It introduces the notion of frames in Krein spaces, extending existing concepts, and establishes their decomposition and relation to orthogonal projections.

Findings

Every frame in a Krein space can be expressed as a sum of three orthonormal bases.

The paper establishes a relationship between frames and orthogonal projections in Krein spaces.

Extension of frame concepts from Hilbert to Krein spaces.

Abstract

In this article we define frame for a Krein space K with a J-orthonormal basis and extend the notion of frame sequence and frame potential analogous to Hilbert spaces.We show that every frame is a sum of three orthonormal bases of a Krein space. We also find relation between frame and orthogonal projections on Krein space.