Abstract
The aim of this article is to give a definition of K-frames in Krein spaces. This definition is compatible with K-frames already known in Hilbert spaces and it generalizes them. We will characterize the K-frames by the synthesis operator and the frame operator, likewise to what is seen in the case of Hilbert spaces. In the rest of the article, we will set a definition of dual sequences and some results concerning this notion. Finally, we will demonstrate how to transfer K-frames for Hilbert spaces to Krein spaces arising from a possibly non-regular Gram operator.
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We would like to thank the referee for carefully reading our manuscript and for giving such constructive comments which helped improving the quality of the paper.
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Communicated by Kasso Okoudjou.
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Mohammed, A., Samir, K. & Bounader, N. K-frames for Krein spaces. Ann. Funct. Anal. 14, 10 (2023). https://doi.org/10.1007/s43034-022-00223-3
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DOI: https://doi.org/10.1007/s43034-022-00223-3