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On the Ideal-Triangularizability of Semigroups of Quasinilpotent Positive Operators on C(K)

Published online by Cambridge University Press:  20 November 2018

M. T. Jahandideh
M. T. Jahandideh*
Affiliation:
Department of Mathematics Dalhousie University Halifax, NS B3H 3J5
*
Current address: School of Mathematics Isfahan University of Technology Isfahan 84156 Iran
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Abstract

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It is known that a semigroup of quasinilpotent integral operators, with positive lower semicontinuous kernels, on ${{L}^{2}}\,(X,\,\mu )$, where $X$ is a locally compact Hausdorff-Lindelöf space and $\mu $ is a $\sigma $-finite regular Borel measure on $X$, is triangularizable. In this article we use the Banach lattice version of triangularizability to establish the ideal-triangularizability of a semigroup of positive quasinilpotent integral operators on $C(\mathbf{K})$ where $\mathbf{K}$ is a compact Hausdorff space.

Keywords

47B65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 298 - 305
Copyright
Copyright © Canadian Mathematical Society 1998

References

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