Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T20:18:29.754Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute values in orthogonally decomposable spaces

Published online by Cambridge University Press:  17 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In an ordered Banach space which is orthogonally decomposable, we define the absolute value and its general properties are given. The results are used to study the properties of linear operators which satisfy Kato's inequality and the locality condition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 215 - 233
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Wolfgang, Arendt, “Kato's inequality and spectral decomposition for positive C 0-groups”, Manuscripta Math. 40 (1982), 277–298.Google Scholar
[2]Wolfgang, Arendt, Chernoff, Paul R. and Kato, Tosio, “A generalization of dissipativity and positive semigroups”, J. Operator Theory 8 (1982), 167–180.Google Scholar
[3]Batty, Charles J.K. and Robinson, Derek W., “Positive one-parameter semigroups on ordered Banach spaces”, Acta Appl. Math. (to appear).Google Scholar
[4]Connes, Alain, “Charactérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann”, Ann. Inst. Fourier (Grenoble) 24 (1974), 121–155.Google Scholar
[5]Gardner, L. Terrell, “Linear maps of C*-algebras preserving the absolute value”, Proc. Amer. Math. Soc. 76 (1979), 293–307.Google Scholar
[6]Kato, T., “Schrodinger operators with singular potentials”, Israel J. Math. 13 (1973), 135–148.CrossRefGoogle Scholar
[7]Nagel, Rainer and Uhlig, Heinrich, “An abstract Kato inequality for generators of positive operator semigroups on Banach lattices”, J. Operator Theory 6 (1981), 113–123.Google Scholar
[8]Robinson, Derek W. and Yamamuro, Sadayuki, “Hereditary cones, order ideals and half-norms”, Pacific J. Math. 110 (1984), 335–343.CrossRefGoogle Scholar
[9]Simon, Barry, “An abstract Kato's inequality for generators of positivity preserving semigroups”, Indiana Univ. Math. J. 26 (1977), 1967–1073.CrossRefGoogle Scholar
[10]Yamamuro, Sadayuki, “On linear operators on ordered Banach spaces”, Bull. Austrai. Math. Soc. 27 (1983), 285–305.Google Scholar
[11]Yamamuro, Sadayuki, “On orthogonally decomposable ordered Banach spaces”, Bull. Austral. Math. Soc. 30 (1984), 357–380.Google Scholar