Fixed point properties of C*-algebras

This paper derives relations between the following properties of a C*-algebra: (i) it has the fpp, (ii) the spectrum of every self-adjoint element is finite, (iii) it is finite dimensional, (iv) it is generated by two projections p and q and the spectrum of p+q is homeomorphic to a compact ordinal α...

Full description

Saved in:
Bibliographic Details
Main Authors: Dhompongsa S., Fupinwong W., Lawton W.
Format: Article
Language:English
Published: 2014
Online Access:http://www.scopus.com/inward/record.url?eid=2-s2.0-77957126516&partnerID=40&md5=8531ac27bace0316969d9894a74ff952
http://cmuir.cmu.ac.th/handle/6653943832/6618
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Chiang Mai University
Language: English
id th-cmuir.6653943832-6618
record_format dspace
spelling th-cmuir.6653943832-66182014-08-30T03:24:24Z Fixed point properties of C*-algebras Dhompongsa S. Fupinwong W. Lawton W. This paper derives relations between the following properties of a C*-algebra: (i) it has the fpp, (ii) the spectrum of every self-adjoint element is finite, (iii) it is finite dimensional, (iv) it is generated by two projections p and q and the spectrum of p+q is homeomorphic to a compact ordinal α<ωω (v) it is generated by two projections and the real Banach algebra generated by every self-adjoint element has the w-fpp, (vi) it has the w-fpp. We prove that (i) implies (ii) using standard fixed point theory, give two proofs that (ii) implies (iii), one based on a result of Ogasawara and another based on geometric properties of projections, and observe that (iii) implies (i) by Brouwer's fixed point theorem. We prove that (iv) implies (v) using the structure of the universal C*-algebra generated by two projections, and discuss a conjecture that ensures (iv) implies (vi). © 2010 Elsevier Inc. 2014-08-30T03:24:24Z 2014-08-30T03:24:24Z 2011 Article 0022247X 10.1016/j.jmaa.2010.08.032 http://www.scopus.com/inward/record.url?eid=2-s2.0-77957126516&partnerID=40&md5=8531ac27bace0316969d9894a74ff952 http://cmuir.cmu.ac.th/handle/6653943832/6618 English
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
language English
description This paper derives relations between the following properties of a C*-algebra: (i) it has the fpp, (ii) the spectrum of every self-adjoint element is finite, (iii) it is finite dimensional, (iv) it is generated by two projections p and q and the spectrum of p+q is homeomorphic to a compact ordinal α<ωω (v) it is generated by two projections and the real Banach algebra generated by every self-adjoint element has the w-fpp, (vi) it has the w-fpp. We prove that (i) implies (ii) using standard fixed point theory, give two proofs that (ii) implies (iii), one based on a result of Ogasawara and another based on geometric properties of projections, and observe that (iii) implies (i) by Brouwer's fixed point theorem. We prove that (iv) implies (v) using the structure of the universal C*-algebra generated by two projections, and discuss a conjecture that ensures (iv) implies (vi). © 2010 Elsevier Inc.
format Article
author Dhompongsa S.
Fupinwong W.
Lawton W.
spellingShingle Dhompongsa S.
Fupinwong W.
Lawton W.
Fixed point properties of C*-algebras
author_facet Dhompongsa S.
Fupinwong W.
Lawton W.
author_sort Dhompongsa S.
title Fixed point properties of C*-algebras
title_short Fixed point properties of C*-algebras
title_full Fixed point properties of C*-algebras
title_fullStr Fixed point properties of C*-algebras
title_full_unstemmed Fixed point properties of C*-algebras
title_sort fixed point properties of c*-algebras
publishDate 2014
url http://www.scopus.com/inward/record.url?eid=2-s2.0-77957126516&partnerID=40&md5=8531ac27bace0316969d9894a74ff952
http://cmuir.cmu.ac.th/handle/6653943832/6618
_version_ 1681420647546224640