Ranges of Bimodule Projections and Conditional Expectations

1. Auflage 2013
ISBN: 978-1-4438-4612-7
Verlag: Cambridge Scholars Publishing

Buch, Englisch, 150 Seiten

The algebraic theory of corner subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e in R) is investigated here in the context of Banach and C*-algebras. We propose a general algebraic approach which includes the notion of ranges of (completely) contractive conditional expectations on C*-algebras and on ternary rings of operators, and we investigate when topological properties are consequences of the algebraic assumptions. For commutative C*-algebras we show that dense corners cannot be proper and that self-adjoint corners must be closed and always have closed complements (and may also have non-closed complements). For C*-algebras we show that Peirce corners and some more general corners are similar to self-adjoint corners. We show uniqueness of complements for certain classes of corners in general C*-algebras, and establish that a primitive C*-algebra must be prime if it has a prime Peirce corner. Further we consider corners in ternary rings of operators (TROs) and characterise corners of Hilbertian TROs as closed subspaces.

Autoren/Hrsg.

Pluta, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Über Autor(innen)

Pluta, Robert
Robert Pluta received his PhD in Mathematics from Trinity College, Dublin, in 2012. He is currently a Visiting Assistant Professor of Mathematics at the University of Iowa. His research interests are in operator algebras and operator spaces.

Robert Pluta received his PhD in Mathematics from Trinity College, Dublin, in 2012. He is currently a Visiting Assistant Professor of Mathematics at the University of Iowa. His research interests are in operator algebras and operator spaces.