59 research outputs found
Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals
In this article we show that the semigroup operation of a strictly linearly
ordered semigroup on a real interval is automatically continuous if each
element of the semigroup admits a square root. Hence, by a result of Acz\'el,
such a semigroup is isomorphic to an additive subsemigroup of the real numbers
Mean ergodicity vs weak almost periodicity
We provide explicit examples of positive and power-bounded operators on
and which are mean ergodic but not weakly almost periodic. As a
consequence we prove that a countably order complete Banach lattice on which
every positive and power-bounded mean ergodic operator is weakly almost
periodic is necessarily a KB-space. This answers several open questions from
the literature. Finally, we prove that if is a positive mean ergodic
operator with zero fixed space on an arbitrary Banach lattice, then so is every
power of .Comment: 10 pages; minor adjustments and three new references included
compared to version
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