### ${\mathcal{L}}_{\pi}$-Spaces and cone summing operators

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.

We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.

We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.

The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour...

Asymptotic convergence theorems for nonnegative operators on Banach lattices, on ${L}^{\infty}$, on C(X) and on ${L}^{p}(1\le p<\infty )$ are proved. The general results are applied to a class of integral operators on L¹.

A new criterion of asymptotic periodicity of Markov operators on ${L}^{1}$, established in [3], is extended to the class of Markov operators on signed measures.