Ranges of bimodule projections and conditional expectations
Citation:
Robert Pluta, 'Ranges of bimodule projections and conditional expectations', [thesis], Trinity College (Dublin, Ireland). School of Mathematics, 2011, pp 150Download Item:
Abstract:
The algebraic theory of comer subrings introduced by Lam (as an abstraction
of the properties of Peirce corners eRe of a ring R associated with an idempotent
e E R) are 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.
Author: Pluta, Robert
Advisor:
Timoney, RichardQualification name:
Doctor of Philosophy (Ph.D.)Publisher:
Trinity College (Dublin, Ireland). School of MathematicsNote:
TARA (Trinity’s Access to Research Archive) has a robust takedown policy. Please contact us if you have any concerns: rssadmin@tcd.ieType of material:
thesisCollections
Availability:
Full text availableKeywords:
Mathematics, Ph.D., Ph.D. Trinity College Dublin.Metadata
Show full item recordLicences: