Abstract
For a two-sided sequence of compact linear operators acting on a Banach space, we consider the notion of spectrum defined in terms of the existence of exponential dichotomies under homotheties of the dynamics. This can be seen as a natural generalization of the spectrum of a matrix—the set of its eigenvalues. We give a characterization of all possible spectra and explicit examples of sequences for which the spectrum takes a form not occurring in finite-dimensional spaces. We also consider the case of a one-sided sequence of compact linear operators.
Funding Statement
The first author and the third author were supported by FCT/Portugal through UID/MAT/04459/2013. The second author was supported in part by the Croatian Science Foundation under the project IP-2014-09-2285 and by the University of Rijeka under the project number 17.15.2.2.01.
Citation
Luis BARREIRA. Davor DRAGIČEVIĆ. Claudia VALLS. "Spectrum for compact operators on Banach spaces." J. Math. Soc. Japan 71 (1) 1 - 17, January, 2019. https://doi.org/10.2969/jmsj/76447644
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