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Graph Groupoids and Partial Isometries
Connection Between Hilbert Space Operators and Graphs
Ilwoo Cho
Livre broché | Anglais
48,45 €
+ 96 points
Description
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.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 92
- Langue:
- Anglais
Caractéristiques
- EAN:
- 9783838313979
- Date de parution :
- 21-05-10
- Format:
- Livre broché
- Format numérique:
- Trade paperback (VS)
- Dimensions :
- 152 mm x 229 mm
- Poids :
- 145 g
