Abstracts: Plenary Speakers
نویسندگان
چکیده
s: Plenary Speakers Spiros Argyros (National Technical University of Athens, Greece) [email protected] HI extensions of L∞ spaces and spaces with very few operators Tuesday, July 30, HA4, 9:00–9:50 We will present a general method of embedding Banach spaces with separable dual into L∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i) For every X with X∗ separable there exists a L∞ space X such that X is isomorphic to a subspace X of X and X/X is Hereditarily indecomposable satisfying the “scalar plus compact” property. (ii) If l1 is not isomorphic to a complemented subspace of X ∗ then the aforementioned X satisfies the “scalar plus compact” property. The above yields that every separable reflexive space embeds into a L∞ space satisfying the “scalar plus compact” property. (Joint work with D. Freeman, R. Haydon, E.Odell, Th. Raikoftsalis, Th. Schlumprecht, D. Zisimopoulou.) Kenneth Davidson (University of Waterloo, Canada) [email protected] The Choquet boundary of an operator system Saturday, August 3, HA4, 9:00–9:50 We solve one of Bill Arveson’s favorite problems: every operator system (and hence every unital operator algebra) has sufficiently many boundary representations to generate the C*-envelope. This was a central question in Arveson’s dilation program left open in his 1969 paper. Arveson solved the separable case recently, but our general solution is also more transparent and in the spirit of the original paper. (This is joint work with Matthew Kennedy.)
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