Pseudo-duals and closeness of continuous g-frames in Hilbert spaces

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Document Type : Original Article

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Department of Mathematics, University of Qom, Qom, Iran

Abstract

‎The paper deals with pseudo-duals of continuous g-frames and their characterizations in Hilbert spaces‎. ‎Mainly‎, ‎the pseudo-duals constructed by bounded operators inserted between the synthesis and analysis operators of the Bessel mappings are considered‎. ‎Duals and approximate duals‎, ‎which are two important classes of pseudo-duals‎, ‎are also studied here‎. ‎Moreover‎, ‎the concepts of closeness and nearness of continuous g-frames are focused and some of their properties are obtained‎. ‎It is shown that there are close relationships between the closeness and nearness of g-frames and their approximate duals‎. ‎Also‎, ‎the above-mentioned concepts are related to the notions of partial equivalence‎, ‎equivalent frames‎, ‎and continuous Riesz-type g-frames.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 28 September 2024

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