Pure Mathematics Colloquium: Marcel de Jeu
Wednesday 10 October 2018, 3:10pm to 4:10pm
Venue
PSC - PSC A54 - View MapOpen to
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Positive representations of algebras of continuous functions
It is well known from linear algebra that a family of mutually commuting normal operators on a finite dimensional complex inner product space can be simultaneously diagonalised. Strongly related to this is the fact that a representation of a commutative C*-algebra on a Hilbert space is generated by a so-called spectral measure, taking its values in the orthogonal projections. A result by Ruoff and the lecturer asserts that a similar phenomenon occurs for positive representations of algebras of continuous functions on a substantial class of Banach lattices.
Recently, it has become clear that these two facts for Hilbert spaces and Banach lattices can be understood from one underlying general theorem for positive homomorphisms of algebras of continuous functions into partially ordered algebras. This result can be proved by purely order-theoretic methods.
In this lecture, we shall explain this theorem and how it relates to the two special cases mentioned above. We shall also sketch the theory of measure and integration in partially ordered vector spaces that is necessary to formulate and establish it.
Speaker
Marcel de Jeu
University of Leiden
Contact Details
Name | Dirk Zeindler |
Telephone number |
+44 1524 593644 |