Geodesic
The spectral properties of weighted homomorphisms in algebras of continuous functions and their applications
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 89-103 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complete description of spectra of noninvertible weighted translation operators in spaces of continuous functions is given. This description yields a criterion of connectedness of the set of positive eigenvalues of a positive operator acting in a space ordered by a cone with an interior point. Some spectral properties of weighted translation operators in uniform algebras are obtained as well. 
@article{ZNSL_1982_107_a5,
     author = {A. K. Kitover},
     title = {The spectral properties of weighted homomorphisms in algebras of continuous functions and their applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--103},
     year = {1982},
     volume = {107},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a5/}
}
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A. K. Kitover. The spectral properties of weighted homomorphisms in algebras of continuous functions and their applications. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 89-103. http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a5/