The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras
Joint Authors
Hoa, Dinh Trung
Osaka, Hiroyuki
Ho, Toan Minh
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-28
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
In the first part of this paper, we show that an AH algebra A=lim→(Ai,ϕi) has the LP property if and only if every element of the centre of Ai belongs to the closure of the linear span of projections in A.
As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott.
The second contribution of this paper is that for an inclusion of unital C*-algebras P⊂A with a finite Watatani index, if a faithful conditional expectation E:A→P has the Rokhlin property in the sense of Kodaka et al., then P has the LP property under the condition thatA has the LP property.
As an application, let A be a simple unital C*-algebra with the LP property, α an action of a finite group G onto Aut(A).
If α has the Rokhlin property in the sense of Izumi, then the fixed point algebra AG and the crossed product algebra A ⋊α G have the LP property.
We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.
American Psychological Association (APA)
Hoa, Dinh Trung& Ho, Toan Minh& Osaka, Hiroyuki. 2013. The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-454240
Modern Language Association (MLA)
Hoa, Dinh Trung…[et al.]. The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-454240
American Medical Association (AMA)
Hoa, Dinh Trung& Ho, Toan Minh& Osaka, Hiroyuki. The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-454240
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454240