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Graph Groupoids and Partial Isometries

 

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  • Product 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.

Product Specifications
SKU :COC31874
AuthorILWOO CHO
LanguageEnglish
BindingPaperback
Number of Pages92
Publishing Year5/21/2010
ISBN978-3838313979
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-29 00:00:00