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On the Structure and Tensor Products of JC-Algebras
- Source :
- Canadian Journal of Mathematics. 35:1059-1074
- Publication Year :
- 1983
- Publisher :
- Canadian Mathematical Society, 1983.
-
Abstract
- Norm closed (or weakly closed) Jordan algebras of self-adjoint operators on a Hilbert space were initially studied by Topping, Effros, and Stormer [15], [4], [12], [13]. These works are very “spatial”, in that the algebras are considered in one given representation. The introduction of their abstract counterparts, the JB- and JBW-algebras, has led to an increased interest in this subject. The author hopes this paper will support the view that a more “space-free” approach is fruitful, even if only the “concrete” algebras are under study. In accordance with this view, a “JC-algebra” in this paper will mean a normed Jordan algebra over the reals, which is isometrically isomorphic to a norm closed Jordan algebra of self-adjoint operators.Some of the results in this paper are closely related to, or rewordings of, results in the above-mentioned papers. However, I feel that the present approach is sufficiently different to be of interest in itself. In particular, many of the technical difficulties associated with earlier approaches are avoided.
- Subjects :
- Pure mathematics
Jordan algebra
Computer Science::Information Retrieval
General Mathematics
010102 general mathematics
Hilbert space
Structure (category theory)
01 natural sciences
symbols.namesake
Tensor product
Norm (mathematics)
0103 physical sciences
symbols
010307 mathematical physics
0101 mathematics
Representation (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 35
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........b7d6f185075252d379439399f40d7dc0