This article is available for purchase or by subscription. See below.
Abstract
|
Let
be a noncommutative,
nonunital
-algebra.
Given a set of commuting positive elements in the corona algebra
, we study
some obstructions to the existence of a commutative lifting of such a set to the multiplier
algebra
.
Our focus is on the obstructions caused by the size of the collection we want to lift. It
is known that no obstacles show up when lifting a countable family of commuting
projections, or of pairwise orthogonal positive elements. However, this is not the case
for larger collections. We prove in fact that for every primitive, nonunital,
-unital
-algebra
,
there exists an uncountable set of pairwise orthogonal positive elements in
such
that no uncountable subset of it can be lifted to a set of commuting elements of
. Moreover, the positive
elements in
can be chosen
to be projections if
has real rank zero.
|
PDF Access Denied
We have not been able to recognize your IP address
3.145.60.149
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
corona algebra, commuting self-adjoint elements, lifting
|
Mathematical Subject Classification 2010
Primary: 47C15
Secondary: 03E75
|
Milestones
Received: 5 February 2017
Revised: 20 March 2019
Accepted: 21 March 2019
Published: 5 November 2019
|
|