Geodesic
Generalized atomic subspaces for operators in Hilbert spaces
Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 325-345.

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We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames. Also, we shall describe the concept of frame operator for a pair of $g$-fusion Bessel sequences and some of their properties.
DOI : 10.21136/MB.2021.0130-20
Classification : 42C15, 46C07
Keywords: frame; atomic subspace; $g$-fusion frame; $K$-$g$-fusion frame 
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Ghosh, Prasenjit; Samanta, Tapas Kumar. Generalized atomic subspaces for operators in Hilbert spaces. Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 325-345. doi : 10.21136/MB.2021.0130-20. http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0130-20/

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