Positive representations




报告题目:Positive representations

报告人: Marcel de Jeu教授 (Leiden University

摘要:Many concrete spaces in analysis are ordered (real) Banach spaces, or even Banach lattices, with groups acting as positive operators on them. One could even argue that such positive group representations are not less natural than unitary group representations in Hilbert spaces, but contrary to the latter they have hardly been studied. The same holds for representations of ordered Banach algebras where a positive element acts as a positive operator. There is an elaborate theory of *-representations of C*-algebras, but far less is known about positive representations of ordered Banach algebras, even though such representations are not rare at all.

We shall indicate what is now known about “positive representations”, and mention some of the main problems. The results (and questions) in this lecture result from collaborations with Garth Dales, Ben de Pagter, Bjorn de Rijk, Yang Deng, Xingni Jiang, David Kok, Miek Messerschmidt, Dusan Radicanin, Mark Roelands, Jan Rozendaal, Frejanne Ruoff, Mayke Straatman, Tony Wickstead, and Marten Wortel.

The talk is meant as an advertisement for the topic and, more generally, for studying groups and Banach (lattice) algebras of operators on Banach lattices. The step from single operator theory on Hilbert spaces to groups and algebras of operators was taken in the first half of the 20th century, and now the field of Positivity could be ripe for a similar development.


报告地点: 第二报告厅



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