Ranges of Bimodule Projections and Conditional Expectations

Robert Pluta (Autor)

Buch | Hardcover

150 Seiten

2013 | Unabridged edition
Cambridge Scholars Publishing (Verlag)
978-1-4438-4612-7 (ISBN)

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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.

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.

Erscheint lt. Verlag	17.5.2013
Verlagsort	Newcastle upon Tyne
Sprache	englisch
Maße	148 x 212 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	1-4438-4612-0 / 1443846120
ISBN-13	978-1-4438-4612-7 / 9781443846127
Zustand	Neuware