Quasicompact and Riesz Composition Endomorphisms of Lipschitz Algebras of Complex-Valued Bounded Functions and Their Spectra

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Abstract

In this paper, we study quasicompact and Riesz composition endomorphisms of Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give some necessary and some sufficient conditions that a composition endomorphism of these algebras to be quasicompact or Riesz. We also establish an upper bound and a formula for the essential spectral radius of a composition endomorphism T of these algebras under some conditions which implies that T is quasicompact or Riesz. Finally, we get a relation for the set of eigenvalues and the spectrum of a quasicompact and Riesz endomorphism of these algebras.

Keywords

Essential spectral radius Lipschitz algebra Quasicompact endomorphism Riesz endomorphism Spectrum 

Mathematics Subject Classification

Primary 46J10 Secondary 47B48 47B38 

Notes

Acknowledgements

The authors would like to thank the referee for her/his very insightful suggestions and comments, in particular, for calling their attention to the Lemma 2.8 of the reference [6], resulted in improving and generalizing the Theorems 2.2 and 2.22.

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor University (PNU)TehranIran
  2. 2.Department of Mathematics, Faculty of ScienceArak UniversityArakIran

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