Abstract
We investigate different possiblities of subspaces of the space \(\ell _{\infty }\) in terms of whether the subspaces are polyhedral or not. We further study finite-dimensional subspaces of \(\ell _{\infty }\) which are of the form \(\ell _\infty ^n\) for some \( n \ge 2.\) As an application of the results we compute the number of extreme contractions for a class of the space of bounded linear operators. In particular we find the number of extreme contractions of \({\mathbb {L}}({\mathbb {X}}, \ell _{\infty }^n),\) where \({\mathbb {X}}\) is a finite-dimensional polyhedral space.
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Acknowledgements
The authors would like to sincerely thank the referee for his/her invaluable suggestions, which lead to substantial improvement of the paper. Dr. Debmalya Sain feels elated to acknowledge the inspiring research vision of Professor Harish Kumar Sardana, the Director of IIIT-Raichur.
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Communicated by Michael Kunzinger.
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The first author would like to thank CSIR, Govt. of India, for the financial support in the form of Junior Research Fellowship under the mentorship of Prof. Kallol Paul.
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Sohel, S., Sain, D. & Paul, K. On subspaces of \(\ell _\infty \) and extreme contractions in \({\mathbb {L}}({\mathbb {X}}, \ell _{\infty }^n)\). Monatsh Math 202, 621–636 (2023). https://doi.org/10.1007/s00605-023-01867-6
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DOI: https://doi.org/10.1007/s00605-023-01867-6