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Graph Groupoids and Partial Isometries: Connection Between Hilbert Space Operators and Graphs
Ilwoo Cho
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Graph Groupoids and Partial Isometries: Connection Between Hilbert Space Operators and Graphs
Ilwoo Cho
In this monograph, we consider the connection between graphs and Hilbert space operators. In particular, we are interested in the algebraic structures, called graph groupoids, embedded in operator algebras. In Part 1, we consider the connection from graphs to partial isometries. Every element in graph groupoids assigns an operator, which is either a partial isometry or a projection, under suitable representations. The von Neumann algebras induced by the dynamical systems of graph groupoids are characterized. In Part 2, we observe the connection from partial isometries to graphs. We show that a finite family of partial isometries on a fixed Hilbert space H creates the corresponding graph, and the graph groupoid of it is an embedded groupoid inside B(H). Moreover, the C*-subalgebra generated by the family is *-isomorphic to the groupoid algebra generated by the graph groupoid of the corresponding graph. As application, we consider the C*-subalagebras generated by a single operator.
Medie | Bøger Paperback Bog (Bog med blødt omslag og limet ryg) |
Udgivet | 21. maj 2010 |
ISBN13 | 9783838313979 |
Forlag | LAP Lambert Academic Publishing |
Antal sider | 92 |
Mål | 225 × 6 × 150 mm · 145 g |
Sprog | Engelsk |