Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Positive derivations on partially ordered linear algebra with an order unit


Authors: Taen Yu Dai and Ralph DeMarr
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] T. Y. Dai, On some special classes of partially ordered linear algebras, J. Math. Anal. Appl. 40 (1972), 649-682. MR 0316342 (47:4890)
  • [2] T. Y. Dai and R. DeMarr, Partially ordered linear algebras with multiplicative diagonal projection map, Trans. Amer. Math. Soc. 224 (1976), 179-187. MR 0419330 (54:7352)
  • [3] R. DeMarr, On partially ordering operator algebras, Canad. J. Math. 19 (1967), 636-643. MR 0212579 (35:3450)
  • [4] R. V. Kadison and J. R. Ringrose, Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 32-63. MR 0206735 (34:6552)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A70, 47B55

Retrieve articles in all journals with MSC: 06A70, 47B55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0491402-4
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, order unit, derivation, generalized nilpotent, matrix algebra, diagonal projection map
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society