Abstract
In this paper, BSE properties of some Banach function algebras are studied. We show that Lipschitz algebras Lipα (X, d) and Dales-Davie algebras D(X, M) are BSE-algebras for certain underlying plane sets X. Moreover, we investigate BSE properties of certain subalgebras of Lipα(X, d)suchas LipA (X, α), Lipn (X, α) and Lip(X, M, α). BSE properties of Bloch type spaces \({{\cal B}_\alpha}\) and Zygmund type spaces Zα are also investigated in different cases of α ∈ ℝ.
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Acknowledgements
The authors are grateful to the anonymous referee whose valuable comments and suggestions improved the manuscript. The authors would like to thank Ali Ulger for his comments on the closedness of the unit ball of BSE-algebras.
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Hosseini, Z.S., Feizi, E. & Sanatpour, A.H. BSE Properties of Some Banach Function Algebras. Anal Math 47, 105–121 (2021). https://doi.org/10.1007/s10476-020-0061-7
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DOI: https://doi.org/10.1007/s10476-020-0061-7
Key words and phrases
- BSE-algebra
- Banach function algebra
- pointwise convergence topology
- Lipschitz algebra
- Dales-Davie algebra
- Bloch type space
- Zygmund type space