Investigating Some Properties of G-frames in Krein Spaces
Keywords:
Krien Space, J-g-frame, G-frame, Frame.Abstract
This paper presents a new definition for g-frames in Kreinspaces, based on the properties of Krein Space. It is shown that a g-frame in a Krein space is also a g-frame in the associated Hilbertspace. However, the converse is not true unless the span of the J-adjoint of positive operators is uniformly J-positive, and the span ofthe J-adjoint of negative operators is uniformly J-negative. The J-g-frame operator is defined for g-frames in Krein spaces, and its properties,such as invertibility and boundedness, are discussed. Additionally, a J-g-dual sequence is introduced for g-frames in Krein spaces and shownto be a g-frame in the associated Hilbert space, but not necessarily inthe Krein space. Finally, the relationship between a g-frame in a Kreinspace and the sequence induced by it in the associated Hilbert space isexamined.Published
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