[Alta-Logic] Peripatetic talk

[Robin Cockett]

Time: 11:0am Wednesday, 30th November

Place: ICT 616

Speaker: Berndt Bremken

Title: Partial isometries

Abstract:

A partial isometry on a Hilbert space is an isometry defined on a closed subspace and mapping the orthogonal complement to zero. Over the past century these basic operators have played a fundamental role in the study of operators, and of algebras of operators, through, for example, the polar decomposition of an operator, the classification of projections and von Neumann algebras, and the K-theory of operator algebras. There has been recent interest in graph C*-algebras which are generated by families of partial isometries with relations determined by the directed edges of a graph. The universal algebra generated by a single partial isometry has not been considered, although special cases are well understood, so algebras generated by a unitary operator, or an isometry. In joint work with Z. Niu we establish a close connection between partial isometries and contractions to examine the algebra generated by a partial isometry.