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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge אלגבראות אופרטורים}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום שלישי, 20 בדצמבר, 2016}
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\textbf{בשעה} \emph{16:00 -- 17:00}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Cuntz-Krieger dilations of Toeplitz-Cuntz-Krieger families via Choquet theory\par}
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תינתן על-ידי
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{\large\scshape Adam Dor-On 
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  (University of Waterloo)
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\textbf{תקציר:}
  Perhaps the simplest dilation result in operator theory is the dilation of an isometry to a unitary. However, when one generalizes an isometry to a Toeplitz-Cuntz-Krieger family of a directed graph, things become much more complicated.

The analogue of a unitary operator in this case is a (full) Cuntz-Krieger family, and a result of Skalski and Zacharias on C\emph{-correspondences supplies us with a such a dilation when the graph is row-finite and sourceless. We apply Arveson`s non-commutative Choquet theory to answer this question for arbitrary graphs. We compute the non-commutative Choquet boundary of graph tensor algebras and are able to recover a result of Katsoulis and Kribs on the computation of the C}-envelope of these algebras.

However, as the non-commutative Choquet boundary of the operator algebra is a more delicate information than the C*-envelope, we are able to dilate any TCK family to a (full) CK family. In fact, we are able to make progress on a decade old problem of Skalski and Zacharias, that asks for the multivariable analogue, generalizing a result of Ito`s dilation theorem. More precisely, we are able to show that TCK families of graphs \$G\_1,\ldots{},G\_d\$ that commute according to a higher rank row-finite sourceless directed graph have CK dilations that still commute according to the higher rank graph structure.
  


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