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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4203

Title: Noncommutative phenomena in measure theory on operators algebras
Authors: Hamhalter, Jan
Issue Date: 2002
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Jan Hamhalter, "Noncommutative phenomena in measure theory on operators algebras ", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 34 (2002), pp. 19-43.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
34 (2002)
Abstract: The aim of this paper is to to review the basic principles of the measure theory built on operator algebras and to summarize recent progress in this field. We concentrate on those results which demonstrate considerable difference between the classical measure theory and its operator-algebraic counterpart. In particular, we show that the functional-analytic structure of a a given operator algebra A, the lattice-theoretic properties of measures on the projection lattice of A, the facial structure of the convex set of all states on A, and the continuity properties of states on A are connected in a way has no analogy in the standard measure theory.
URI: http://hdl.handle.net/10077/4203
ISSN: 0049-4704
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.34 (2002)

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