Geodesic
Controlled $g$-atomic subspaces for operators in Hilbert spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 17-33

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Controlled $g$-atomic subspace for a bounded linear operator is being presented and a characterization has been given. We give an example of controlled $K$-$g$-fusion frame. We construct a new controlled $K$-$g$-fusion frame for the Hilbert space $H \oplus X$ using the controlled $K$-$g$-fusion frames of the Hilbert spaces $H$ and $X$. Several useful resolutions of the identity operator on a Hilbert space using the theory of controlled $g$-fusion frames have been discussed. We introduce the frame operator for a pair of controlled $g$-fusion Bessel sequences.
Keywords: $K$-$g$-fusion frame, $g$-atomic subspace, frame operator, controlled $g$-fusion frame, controlled $K$-$g$-fusion frame. 
@article{IVM_2022_12_a1,
     author = {Prasenjit Ghosh and T. K. Samanta},
     title = {Controlled $g$-atomic subspaces for operators in {Hilbert} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {17--33},
     publisher = {mathdoc},
     number = {12},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_12_a1/}
}
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Prasenjit Ghosh; T. K. Samanta. Controlled $g$-atomic subspaces for operators in Hilbert spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 17-33. http://geodesic.mathdoc.fr/item/IVM_2022_12_a1/