Mathematica Bohemica, Vol. 147, No. 3, pp. 325-345, 2022
Generalized atomic subspaces for operators in Hilbert spaces
Prasenjit Ghosh, Tapas Kumar Samanta
Received July 24, 2020. Published online August 4, 2021.
Abstract: 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.
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Affiliations: Prasenjit Ghosh, Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India, e-mail: prasenjitpuremath@gmail.com; Tapas Kumar Samanta, Department of Mathematics, Uluberia College, Uluberia, Howrah, 711315, West Bengal, India, e-mail: mumpu_tapas5@yahoo.co.in
