Research Information System
INDAGATIONES MATHEMATICAE-NEW SERIES, vol.32, no.4, pp.861-882, 2021 (SCI-Expanded, Scopus)
A positive operator T : E -> E on a Banach lattice E with an order continuous norm is said to be B-Volterra with respect to a Boolean algebra B of order projections of E if the bands canonically corresponding to elements of B are left fixed by T. A linearly ordered sequence xi in B connecting 0 to 1 is called a forward filtration. A forward filtration can be used to lift the action of the B-Volterra operator T from the underlying Banach lattice E to an action of a new norm continuous operator (T) over cap (xi) : M-r (xi). M-r (xi) on the Banach lattice M-r (xi) of regular bounded martingales on E corresponding to.. In the present paper, we study properties of these actions. The set of forward filtrations are left fixed by a function which erases the first order projection of a forward filtration and which shifts the remaining order projections towards 0. This function canonically induces a norm continuous shift operator s between two Banach lattices of regular bounded martingales. Moreover, the operators (T) over cap (xi) and s commute. Utilizing this fact with inductive limits, we construct a categorical limit space M-T,M-xi which is called the associated space of the pair (T, xi). We present new connections between theories of Boolean algebras, abstract martingales and Banach lattices. (C) 2021 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.