Journal article
The Banach-Lie algebra of multiplication operators on a JBW*-triple
- Abstract:
- The Banach-Lie algebra L (A) of multiplication operators on the JB*-triple A is introduced and it is shown that the hermitian part L (A)h of L (A) is a unital GM-space the base of the dual cone in the dual GL-space (L (A)h)* of which is affine isomorphic and weak*-homeomorphic to the state space of L (A). In the case in which A is a JBW*-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space L (A)h satisfy0 ≤ D (u, u) + D (v, v) ≤ idA, and that u is a pre-associate of v if and only ifD (u, u) ≤ D (v, v) . © 2008 Elsevier Inc. All rights reserved.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 238.2KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jfa.2008.02.005
Authors
+ King Saud University, Riyadh
More from this funder
- Funding agency for:
- Edwards, C
- Grant:
- 2316038497
- Publisher:
- Elsevier
- Journal:
- JOURNAL OF FUNCTIONAL ANALYSIS More from this journal
- Volume:
- 254
- Issue:
- 11
- Pages:
- 2866-2892
- Publication date:
- 2008-06-01
- DOI:
- EISSN:
-
1096-0783
- ISSN:
-
0022-1236
- Language:
-
English
- Keywords:
- Pubs id:
-
5847
- UUID:
-
uuid:08667051-7f70-42d0-90f2-523318bc1c1b
- Local pid:
-
pubs:5847
- Source identifiers:
-
5847
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 2008
- Notes:
- Copyright 2008 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
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