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This collection of surveys is an out?ow from the 2006 conference Carthapos06 in Tunis (Tunisia). Apart from regular conference talks, ?ve survey talks formed the core of a workshop in Positivity, supported by the National Science Foun- tion.Theconferenceorganizers(KarimBoulabiar,GerardBuskes,andAbdelmajid Triki) decided to expand on the idea of core surveys and the nine surveys in this book are the harvest from that idea. Positivity derives from an order relation. Order relations are the mathem- ical tool for comparison. It is no surprise that seen in such very general light, the historyof Positivityis ancient.Archimedes,certainly,hadthe veryessenceofpo- tivityinmindwhenhediscoveredthelawofthelever.Hismethodofexhaustionto calculate areas uses a principle that nowadays carries his name, the Archimedean property. The surveys in this book are slanted into the direction that Archimedes took.Functionalanalysisisheavilyrepresented.Butthereismore.Latticeordered groupsappearinthearticlebyMartinezinthemodernjacketofframes.Henriksen and Banerjee write their survey on rings of continuous functions. Blecher and de Pagterineachoftheirpaperssurveypartsofnon-commutativefunctionalanalysis. Positiveoperatorsare the main topic in the papers by Curbera and Ricker, Schep, and Wickstead. And positive bilinear maps are the protagonists in the survey by Bu, Buskes, and Kusraev. The conference organizers (and editors of this volume) write about f-algebras. Carthapos06 was more than just a conference and workshop in Africa. It brought together researchers in Positivity from many directions of Positivity and form many corners of the world. This book can be seen as a culmination of their paths meeting in Tunisia, Africa.

Economics --- Ordered algebraic structures --- Differential topology --- Operator theory --- Functional analysis --- Mathematical analysis --- algebra --- analyse (wiskunde) --- functies (wiskunde) --- economie --- topologie