Morteza Mirzaee Azandaryani. Source: Annals of Functional Analysis, Volume 10, Number 4, 525--536.Abstract:
In the following we show that, under some conditions, $\varphi$ -morphisms preserve duals and approximate duals of frames in Hilbert $C^{\ast }$ -modules. Moreover, using $\varphi $ -morphisms and some concepts related to frame theory such as modular Riesz bases, canonical duals, tensor products, and Bessel multipliers, we construct new approximate duals, considering in particular the approximate duals constructed by compact operators and morphisms.