On invariant functions and ergodic measures of Markov operators on C(X)
On the lattice properties of invariant functions for Markov operators on C(X)
Most Markov operators on C(X) are quasi-compact and uniquely ergodic
On the lattice boundary of Markov operators
Krengel-Lin decomposition for noncompact groups
Structure of mixing and category of complete mixing for stochastic operators
Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak...
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