|
|
Автор: ILWOO CHO
Год: 2010
Издание:
LAP Lambert Academic Publishing
Страниц: 92
ISBN: 9783838313979
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...
|
|
ILWOO CHOGraph Groupoids and Partial Isometries
Wawrzynczyk A.Group representations and special functions
Joiner Associates StaffHow to Graph Plain and Simple (Student Edition)