Boundary Representations of Operator Spaces, and Compact Rectangular Matrix Convex Sets

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Date
2016-12-13MFO Scientific Program
OWLF 2016Series
Oberwolfach Preprints;2016,24Author
Fuller, Adam H.
Hartz, Michael
Lupini, Martino
Metadata
Show full item recordOWP-2016-24
Abstract
We initiate the study of matrix convexity for operator spaces. We define the notion of compact rectangular matrix convex set, and prove the natural analogs of the Krein-Milman and the bipolar theorems in this context. We deduce a canonical correspondence between compact rectangular matrix convex sets and operator spaces. We also introduce the notion of boundary representation for an operator space, and prove the natural analog of Arveson's conjecture: every operator space is completely normed by its boundary representations.
This yields a canonical construction of the triple envelope of an operator space.