Positive derivations on partially ordered linear algebra with an order unit
HTML articles powered by AMS MathViewer
- by Taen Yu Dai and Ralph DeMarr PDF
- Proc. Amer. Math. Soc. 72 (1978), 21-26 Request permission
Abstract:
We show that the range of a positive derivation on a Dedekind $\sigma$-complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.References
- Taen-yu Dai, On some special classes of partially ordered linear algebras, J. Math. Anal. Appl. 40 (1972), 649–682. MR 316342, DOI 10.1016/0022-247X(72)90011-X
- Taen Yu Dai and Ralph DeMarr, Partially ordered linear algebras with multiplicative diagonal map, Trans. Amer. Math. Soc. 224 (1976), 179–187. MR 419330, DOI 10.1090/S0002-9947-1976-0419330-3
- Ralph DeMarr, On partially ordering operator algebras, Canadian J. Math. 19 (1967), 636–643. MR 212579, DOI 10.4153/CJM-1967-057-6
- Richard V. Kadison and John R. Ringrose, Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 32–63. MR 206735
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 21-26
- MSC: Primary 06A70; Secondary 47B55
- DOI: https://doi.org/10.1090/S0002-9939-1978-0491402-4
- MathSciNet review: 0491402