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Picture of Ranges of Bimodule Projections and Conditional Expectations

Ranges of Bimodule Projections and Conditional Expectations

Author(s): Robert Pluta

Book Description

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.


ISBN-13: 978-1-4438-4612-7
ISBN-10: 1-4438-4612-0
Date of Publication: 01/04/2013
Pages / Size: 150 / A5
Price: £39.99


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.