Duality and Preservition of Continuous k-j-Frames in Krein Spaces
Atmani Mohammed, Samir Kabbaj · Azerbaijan Journal of Mathematics · 2025
The purpose of this paper is to introduce and study the notion of continuous K-frames in the Krein space setting under the name continuous K-J-frames.We will also present the definition of K-J-dual continuous Bessel family and some results concerning this notion.The preservation of the continuous K-J-frames by usual operations (the composition by a bounded operator, the sum) will also be studied.Finally, we will see how to achieve a transfer of continuous K-frames from a Hilbert space to a Krein space arising from a possibly non-regular Gram operator.