<abstract xmlns="http://www.w3.org/1999/xhtml"><p><italic>K</italic>-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled <italic>K</italic>-fusion frames, and we develop some results on the controlled <italic>K</italic>-fusion frames for Hilbert spaces, which generalize some well known results of controlled fusion frame case. Also we discuss some characterizations of controlled Bessel <italic>K</italic>-fusion sequences and of controlled <italic>K</italic>-fusion frames. Further, we analyze stability conditions of controlled <italic>K</italic>-fusion frames under perturbation.</p></abstract>

K-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K-fusion frames, and we develop some results on the controlled K-fusion frames for Hilbert spaces, which generalize some well known results of controlled fusion frame case. Also we discuss some characterizations of controlled Bessel K-fusion sequences and of controlled K-fusion frames. Further, we analyze stability conditions of controlled K-fusion frames under perturbation.

Controlled <italic>K</italic>-Fusion Frame for Hilbert Spaces

Laboratory of Partial Differential Equations, Algebra and Spectral Geometry, Department of Mathematics, Faculty of Sciences

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Controlled -Fusion Frame for Hilbert Spaces

{"article-title":{"italic":"K","content":["Controlled","-Fusion Frame for Hilbert Spaces"]}}

K-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K-fusion...

Controlled K-Fusion Frame for Hilbert Spaces

Published Online: Dec 14, 2020

Page range: 116 - 133

Received: Jul 07, 2020

Accepted: Nov 18, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0011

Keywords
Fusion Frame, -Fusion Frame, Controlled Fusion Frame, Stability

© 2020 Nadia Assila et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Controlled K-Fusion Frame for Hilbert Spaces

Published Online: Dec 14, 2020

Page range: 116 - 133

Received: Jul 07, 2020

Accepted: Nov 18, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0011

KeywordsFusion Frame, -Fusion Frame, Controlled Fusion Frame, Stability

© 2020 Nadia Assila et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Fusion Frame, -Fusion Frame, Controlled Fusion Frame, Stability