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Controlled g-Atomic Subspaces for Operators in Hilbert Spaces

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Abstract

A controlled \(g\)-atomic subspace for a bounded linear operator is 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 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.

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Authors and Affiliations

  1. University of Calcutta, 700019, Kolkata, West Bengal, India

    Prasenjit Ghosh

  2. Uluberia College, 711315, Uluberia, Howrah West Bengal, India

    Tapas K. Samanta

Authors
  1. Prasenjit Ghosh
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  2. Tapas K. Samanta
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Correspondence to Prasenjit Ghosh or Tapas K. Samanta.

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Prasenjit Ghosh, Tapas K. Samanta Controlled g-Atomic Subspaces for Operators in Hilbert Spaces. Russ Math. 66, 16–32 (2022). https://doi.org/10.3103/S1066369X22120064

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