A Coanalytic Rank on Super-Ergodic Operators

Details A Coanalytic Rank on Super-Ergodic Operators A Coanalytic Rank on Super-Ergodic Operators

2009-12-29

arxiv.org/abs/0912.5389v1

Mathematics

General Topology

9 pages

Scientific paper

Techniques from Descriptive Set Theory are applied in order to study the Topological Complexity of families of operators naturally connected to ergodic operators in infinite dimensional Banach Spaces. The families of ergodic, uniform-ergodic,Cesaro-bounded and power-bounded operators are shown to be Borel sets, while the family of super-ergodic operators is shown to be either coanalytic or Borel according to specific structures of the Space. Moreover, trees and coanalytic ranks are introduced to characterize super-ergodic operators as well as spaces where the above classes of operators do not coincide.

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