IJMMSInternational Journal of Mathematics and Mathematical Sciences1687-04250161-1712Hindawi Publishing Corporation13254110.1155/2011/132541132541Research ArticleIsometric and Closed-Range Composition Operators between Bloch-Type SpacesZorboskaNinazorbosk@cc.umanitoba.caAraiAsaoDepartment of MathematicsUniversity of ManitobaWinnipeg, MBCanadaR3T 2N2umanitoba.ca20113052011201116112010300320112011Copyright © 2011 Nina Zorboska.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.