Some Inequalities-Equalities Concerning Continuous Generalized Fusion Frames in Hilbert Spaces

Year 2024, Volume: 14 Issue: 2, 160 - 180, 31.07.2024

Nadia Assila Samir Kabbej , Ouafaa Bouftouh Chaimae Mezzat Choonkil Park

Abstract

Continuous generalized fusion frame theory was recently introduced by Rahimi et al. [14]. Several equalities and inequalities have been obtained for frame, fusion generalized fusion frame, among others. In the present paper, we continue and extend these results to obtain some important identities and inequalities in the case of continuous generalized fusion frame, Parseval continuous generalized fusion frame, λ-tight continuous generalized fusion frame. Moreover, we obtain some new inequalities for the alternate
dual continuous generalized fusion frame. Finally, we obtain frame operator of a pair of
Bessel continuous generalized fusion mapping and we derive some results about resolution
of identity.

Keywords

continuous generalized fusion Frame, Parseval continuous generalized fusion frame, tight continuous generalized fusion frame, resolution of identity

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