In this paper, we study quasicompact and Riesz composition operators on Banach spaces of Lipschitz–Hölder functions on pointed metric spaces. For a composition operator T on these spaces, we give an upper bound for \(r_e(T)\), the essential spectral radius of T, and establish a formula for \(r_e(T)\) whenever metric spaces are compact. We also give some necessary and some sufficient conditions that a composition operator T on these spaces to be quasicompact or Riesz. Finally, we get a relation for the set of eigenvalues and the spectrum of a quasicompact and Riesz composition operator on these spaces.
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The authors would like to thank the referee for carefully reading the paper and his/her invaluable comments and suggestions. This research was in part supported by a grant from Arak University (no. 97/2321). The authors would like to thank this support.
Communicated by Martin Mathieu.
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Alimohammadi, D., Mayghani, M. Quasicompact and Riesz composition operators on Banach spaces of Lipschitz functions on pointed metric spaces. Adv. Oper. Theory (2020). https://doi.org/10.1007/s43036-020-00093-3
- Essential norm
- Essential spectral radius
- Pointed metric space
- Quasicompact operator
- Riesz operator
Mathematics Subject Classification