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Report Hosseini 2015

"During my stay I had regular interactions with Professor Juan J. Font on some preserving problems in the context of function spaces. In fact, preserving problems concern the question of determining or describing the general form of all trans- formations of a given structure which preserve something in connection with the underlying structure such as norm, spectrum, spectral-radius, etc. For instance, we can point out the famous Banach-Stone theorem which characterizes linear isome- tries between C(X)-spaces as weighted composition operators. We first continued our study on real version of multi-linear isometries, and nowadays we have been doing our final revisions on this research project. 
Moreover, working on diameter preserving maps was another main schedule. This research visit provided a fruitful collaboration, and our papers are listed as follows:

• M. Hosseini, J.J. Font, Multi-real-linear isometries on function algebras, submitted

• M. Hosseini, J.J. Font, On diameter preserving maps, preprint"

-Maliheh Hosseini