In the present paper, we obtain some necessary, sufficient and equivalent conditions for some special sequences in a Hilbert $C^{\ast}$-module to constitute a standard g-Bessel sequence or a K-g-frame, where K is an adjointable operator on the underlying Hilbert $C^{\ast}$-module. Mainly, it is shown that standard g-Bessel sequences and K-g-frames are stable under the different kinds of perturbations. Then, as a special kind of K-duals for a standard g-frame, its $\alpha$-duals are considered and characterized ($\alpha$ is an integer). Moreover, we get some conditions under which standard g-Bessel sequences, K-g-frames and $\alpha$-duals are preserved under the action of adjointable operators.
Zamani Mirarkoulaei, F. & Mirzaee Azandaryani, M. (2026). Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules. (e6031). AUT Journal of Mathematics and Computing, (), e6031 https://doi.org/10.22060/ajmc.2025.24558.1438
MLA
Zamani Mirarkoulaei, F., & Mirzaee Azandaryani, M. "Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules" .e6031 , AUT Journal of Mathematics and Computing, , 2026, e6031. doi: 10.22060/ajmc.2025.24558.1438
HARVARD
Zamani Mirarkoulaei, F., & Mirzaee Azandaryani, M. (2026). 'Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules', AUT Journal of Mathematics and Computing, (), e6031. doi: 10.22060/ajmc.2025.24558.1438
CHICAGO
Zamani Mirarkoulaei, F. & Mirzaee Azandaryani, M., "Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules." AUT Journal of Mathematics and Computing, (2026): e6031, doi: 10.22060/ajmc.2025.24558.1438
VANCOUVER
Zamani Mirarkoulaei F., Mirzaee Azandaryani M. Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules. AUT J Math Comput. 2026;():e6031. doi: 10.22060/ajmc.2025.24558.1438
