Frames and Dual Frames for Krein Spaces

Abstract

In last decades, the operator theory of Krein spaces, Krein space approaches, and various generalizations of frames have interested many mathematicians due to their potential applications in mathematics and engineering. This paper addresses the frame theory for Krein spaces. We present some properties of J-orthonormal bases, Parseval frames and frames for Krein spaces, and a parametric expression of all duals of an arbitrarily given frame in Krein spaces. This study shows that the frame theory for Krein spaces is not a direct generalization of the frame theory for Hilbert spaces.

Keywords:

• Frame
• Krein space
• dual frame
• J-orthonormal basis
• Parseval frame

2020 MS Classification:

• 42C15
• 46C20
• 47B50

Disclosure statement

No competing interest.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 12371091).