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

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the range of a positive derivation on a Dedekind -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.

**[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)**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0491402-4

Keywords:
Dedekind -complete partially ordered linear algebra,
order unit,
derivation,
generalized nilpotent,
matrix algebra,
diagonal projection map

Article copyright:
© Copyright 1978
American Mathematical Society