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On the ideal-triangularizability of semigroups of quasinilpotent positive operators on $C({\cal K})$ |
Canad. Math. Bull. 41(1998), 298-305
Published:1998-09-01
Printed: Sep 1998
Printed: Sep 1998
- M. T. Jahandideh
Abstract
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-Lindel\"of 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
$C({\cal K})$ where ${\cal K}$ is a compact Hausdorff space.
| MSC Classifications: | 47B65 - Positive operators and order-bounded operators |