The “zero-two” law in Orlicz-Kantorovich spaces. (English) Zbl 1535.37007
Vector-valued versions of ‘zero-two’ laws giving criteria for successive iterates of an operator to converge in norm are proved in the setting of Orlicz-Kantorovich spaces. The history and context for results of this shape is briefly described, and the paper uses the language of Boolean algebras, Riesz spaces, vector integration, lattice-normed spaces, and measurable bundles of Boolean algebras and Banach lattices.
Reviewer: Thomas B. Ward (Durham)
MSC:
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 47A35 | Ergodic theory of linear operators |
| 46B42 | Banach lattices |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46G10 | Vector-valued measures and integration |
Keywords:
zero-two law; \(L_0\)-valued measure; Orlicz-Kantorovich spaces; measurable Banach bundle; positive contractionsReferences:
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