A general differentiation theorem for multiparameter additive processes
Tom 91 / 2002
Colloquium Mathematicum 91 (2002), 143-155
MSC: Primary 47A35, 47D03, 46E30.
DOI: 10.4064/cm91-1-10
Streszczenie
Let $(L,\| \cdot \| _{L})$ be a Banach lattice of equivalence classes of real-valued measurable functions on a $\sigma $-finite measure space and $T=\{ T(u):u=(u_{1}, \dots,u_{d})$, $u_{i}>0$, $1\leq i\leq d\} $ be a strongly continuous locally bounded $d$-dimensional semigroup of positive linear operators on $L$. Under suitable conditions on the Banach lattice $L$ we prove a general differentiation theorem for locally bounded $d$-dimensional processes in $L$ which are additive with respect to the semigroup $T$.
