This is an announcement for the paper "A coanalytic rank on super-ergodic operators" by Mohammed Yahdi. Abstract: 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. Archive classification: math.GN math.FA Mathematics Subject Classification: 47A35; 54H05 Remarks: 9 pages The source file(s), YahdiCoanalyticRankOnSuperErgodicOperators.tex: 28531 bytes, is(are) stored in gzipped form as 0912.5389.gz with size 9kb. The corresponding postcript file has gzipped size 80kb. Submitted from: myahdi@ursinus.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.5389 or http://arXiv.org/abs/0912.5389 or by email in unzipped form by transmitting an empty message with subject line uget 0912.5389 or in gzipped form by using subject line get 0912.5389 to: math@arXiv.org.