Final Activity Report Summary - UNCONDITIONAL (Unconditionality and Geometrical Properties of Polynomials on Banach Lattices) The two years spent by the fellow in the 'Departamento de analisis matematico' of the University of Valencia had several important results. Three research articles, written in collaboration with four mathematicians, two being the members of the research team to whom the fellow belonged in Valencia and the others from Madrid were finalised and submitted for publication. Another five articles, in collaboration with eight mathematicians from Valencia, Granada, Madrid, Galway in Ireland and Kyungpook in Korea were in the process of being written by the time of the project completion and they were expected to be finalised in due time. The fellow was an invited speaker at two renowned international conferences in his field of work, in Madrid and Caceres, and was a participant in other two, one in Murcia and one in Valencia. Among the effects of this exposure several invitations to be a speaker in analysis seminars at various universities could be counted, such as Dublin in Ireland, Lille in France, Granada and, of course, Valencia. His research, which was strongly supported by the team at the host institution, involved academic visits to other universities, namely Galway, Mons in Belgium, Granada and Madrid. Two of the above mentioned articles took shape during these visits. Connections with the previous institutions where the fellow studied, i.e. Al .I. Cuza University in Iasi, Romania and National University of Ireland (NUI) in Galway were maintained or reinforced through of several academic visits which set plans for future collaborations. As part of the research team to whom the fellow and the scientist in charge belonged, they got actively involved in the setting up and running of the 'Murcia Valencia functional analysis meetings'. The first two of them took place in January and May 2007, with the fellow being one of the speakers at the first one, hosted by Universidad Politecnica de Valencia. This involvement contributed to a significant improvement in the fellow's organisational and communicational skills, apart from the obvious scientific benefit that he experienced via all the academic contacts and exposure which were assured by the host institution during the two years of this intra-European fellowship. Since the Marie Curie fellowship represented just a step in his career, the fellow made a few career exploratory visits in order to open up new avenues for his future as an active mathematician. The first, in June 2006, was at the University of Cambridge where the fellow met a young member of the mathematics department, Dr Richard Smith, who collaborated personally in his research with mathematicians from the host institution. This was followed, in July 2006, by two equally important encounters, one of them in Dublin, with Prof. Sean Dineen, the worldwide leader of the fellow's research area and the other one in Iasi, Romania, at the university where the fellow obtained his BSc degree and where he met the Head of the mathematics faculty, Prof. Ovidiu Carja. The itinerary culminated with the attendance of a job interview at the end of August 2006 at Queen's University of Belfast. The subsequent offer to take up a post of lecturer and be a member of the Pure Mathematics Research Centre of the above named University was arguably the most important achievement of this fellowship, since it was certainly an official recognition of the fellow's strength in research.