Abstract
To study the notion of gap between two operator matrices on non-Archimedean Banach spaces, it is natural to take stability of closedness for these matrices into account due to the definitions of \(\mathbb {K}\)-diagonally dominant and off-\(\mathbb {K}\)-diagonally dominant operator matrices. So, we shall study this problem in the present paper. Furthermore, under sufficient conditions, we give a counterpart of the generalized convergence for a operator matrix.
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Acknowledgements
The authors are grateful to Professor Bertin Diarra for enhancing this work.
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Ammar, A., Lazrag, N. A formula for gap between \(\mathbb {K}\)-relatively bounded operator matrices in non-Archimedean Banach spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 2469–2497 (2023). https://doi.org/10.1007/s12215-022-00807-x
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DOI: https://doi.org/10.1007/s12215-022-00807-x
Keywords
- Non-Archimedean Banach space
- \(\mathbb {K}\)-relatively
- Matrix of linear operator
- Gap
- Generalized convergence