Open Access
January, 2019 Spectrum for compact operators on Banach spaces
J. Math. Soc. Japan 71(1): 1-17 (January, 2019). DOI: 10.2969/jmsj/76447644


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


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Luis BARREIRA. Davor DRAGIČEVIĆ. Claudia VALLS. "Spectrum for compact operators on Banach spaces." J. Math. Soc. Japan 71 (1) 1 - 17, January, 2019.


Received: 25 October 2016; Revised: 12 May 2017; Published: January, 2019
First available in Project Euclid: 14 September 2018

zbMATH: 07056555
MathSciNet: MR3910544
Digital Object Identifier: 10.2969/jmsj/76447644

Primary: 37D99

Keywords: ‎compact‎ ‎operators , exponential dichotomies , spectra

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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