Skip to main content Accessibility help
×
Home

Spectral and asymptotic properties of dominated operators

  • Frank Räbiger (a1) and Manfred P. H. Wolff (a1)

Abstract

We investigate the relationship between the peripheral spectrum of a positive operator T on a Banach lattice E and the peripheral spectrum of the operators S dominated by T, that is, ]Sx] ≤ T]x] for all x ε E. This can be applied to obtain inheritance results for asymptotic properties of dominated operators.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Spectral and asymptotic properties of dominated operators
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Spectral and asymptotic properties of dominated operators
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Spectral and asymptotic properties of dominated operators
      Available formats
      ×

Copyright

References

Hide All
[1]Aliprantis, C. D. and Burkinshaw, O., ‘On weakly compact operators on Banach lattices’, Proc. Amer. Math. Soc. 83 (1981), 573578.
[2]Aliprantis, C. D., Positive operators (Academic Press, London, 1985).
[3]Andreu, F., Caselles, V., Martinz, J. and Mazon, J. M., ‘The essential specturm of AM-compact operators’, Indag. Math. (N.S.) 2 (1991), 149158.
[4]Bukhvalov, A. V., ‘Integral representations of linear operators’, J. Soviet. Math. 8 (1978), 129137.
[5]Caselles, V., ‘On the peripheral spectrum of positive operators’, Israel J. Math. 58 (1987), 144160.
[6]Clément, Ph., Heijmans, H. J. A. M., Angenent, S., van Duijn, C. J. and de Pagter, B., One-parameter semigroups (North-Holland, Amsterdam, 1987).
[7]Dodds, P. G. and Fremlin, D. H., ‘Compact operators in Banach lattices’, Israel J. Math. 34 (1979), 287320.
[8]Dunford, N., ‘Spectral theory. I Convergence to projections’, Trans. Amer. Math. Soc. 54 (1943), 185217.
[9]Eberlein, W. F., ‘Abstract ergodic theorems and weak almost periodic functions’, Trans. Amer. Math. Soc. 67 (1949), 217240.
[10]Emilion, R., ‘Mean bounded operators and mean ergodic theorems’, J. Funct. Anal. 61 (1985), 114.
[11]Gohberg, I., Goldberg, S. and Kaashoek, M. A., Classes of linear operators, 1 (Birkhäuser, Basel, 1990).
[12]Greiner, G., Über das Spektrum stark stetiger Halbgruppen positiver Operatoren (Dissertation, Tübingen, 1980).
[13]Haid, W., Sätze vom Radon-Nikodym-Typ für Operatoren auf Banachverbänden (Dissertation, Tübingen, 1982).
[14]Kalton, N. J. and Saab, P., ‘Ideal properties of regular operators between Banach lattices’, Illinois J. Math. 29 (1985), 382400.
[15]Katznelson, Y. and Tzafriri, L., ‘On power bounded operators’, J. Funct. Anal. 68 (1986), 313328.
[16]Krengel, U., Ergodic theorems (de Gruyter, Berlin, 1985).
[17]Martinez, J., ‘The essential spectral radius of dominated positive operators’, Proc. Amer. Math. Soc. 118 (1993), 419426.
[18]Martinez, J. and Mazon, J. M., ‘Quasi-compactness of dominated positive operators and C 0-semi-groups’, Math. Z. 207 (1991), 109120.
[19]Meyer-Nieberg, P., Banach lattices (Springer, Berlin, 1991).
[20]de Pagter, B., ‘The components of a positive operator’, Indag. Math. 86 (1983), 229241.
[21]de Pagter, B. and Schep, A. R., ‘Measures of non-compactness of operators on Banach lattices’, J. Funct. Anal. 78 (1988), 3155.
[22]Räbiger, F., Absolutstetigkeit und Ordnungsabsolutstetigkeit von Operatoren, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Math.-Naturwiss. Klasse, Jahrgang 1991, 1. Abhandlung, 1132, (Springer, Berlin, 1991).
[23]Räbiger, F., ‘Stability and ergodicity of dominated semigroups, I. The uniform case’, Math. Z. 214 (1993), 4354.
[24]Räbiger, F., ‘Stability and ergodicity of dominated semigroups, II. The strong case’, Math. Ann. 297 (1993), 103116.
[25]Räbiger, F., ‘Attractors and asymptotic periodicity of positive operators on Banach lattices’, Forum Math. 7 (1995), 665683.
[26]Schaefer, H. H., Banach lattices and positive operators (Springer, Berlin, 1974).
[27]Schep, A. R., Kernel operators (Ph. D. Thesis, University of Leiden, Netherlands, 1977).
[28]Zaanen, A. C., Riesz spaces II (North-Holland, Amsterdam, 1983).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed