K-frames for Krein spaces

被引：0
作者：
Atmani Mohammed
Kabbaj Samir
Nourdine Bounader
机构：
[1] University of Ibn Tofail,Department of Mathematics
来源：
Annals of Functional Analysis | 2023年 / 14卷
关键词：
-frames; -dual Bessel sequences; Krein spaces; Non-regular Gram operator; 42C15; 46C20;
D O I：
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学科分类号：
摘要：
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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