Abstract
In this article, we investigate some general properties of the multiplier algebras of normed spaces of continuous functions (NSCF). In particular, we prove that the multiplier algebra inherits some of the properties of the NSCF. We show that it is often possible to construct NSCF’s which only admit constant multipliers. To do that, using a method from Mashreghi and Ransford (Anal Math Phys 9(2):899–905, 2019), we prove that any separable Banach space can be realized as a NSCF over any separable metrizable space of infinite cardinality. On the other hand, we give a sufficient condition for non-separability of a multiplier algebra.
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Acknowledgements
The author would like to thank Yemon Choi who contributed Example 4.2, Jochen Wengenroth and Giorgio Metafune, who contributed to the proof of Lemma 5.15, and the service MathOverflow which made it possible. The author would also like to express gratitude towards José Bonet, who brought the author’s attention to the papers [18, 27]. Finally, the author also wants to acknowledge the anonymous reviewer whose the suggestions significantly increased clarity of exposition.
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Bilokopytov, E. Multiplier Algebras of Normed Spaces of Continuous Functions. Mediterr. J. Math. 18, 256 (2021). https://doi.org/10.1007/s00009-021-01888-1
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DOI: https://doi.org/10.1007/s00009-021-01888-1