Mathematica Bohemica, first online, pp. 1-21


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.
Keywords:  frame; atomic subspace; $g$-fusion frame; $K$-$g$-fusion frame
Classification MSC:  42C15, 46C07
DOI:  10.21136/MB.2021.0130-20

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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


 
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