A class of partially ordered linear algebras
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- by Ralph DeMarr PDF
- Proc. Amer. Math. Soc. 39 (1973), 255-260 Request permission
Abstract:
We consider a special type of partially ordered linear algebra which is like an algebra of real-valued functions. We show that various natural properties characterize this type of algebra. These natural properties relate the algebraic and order structures to each other.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- 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
- Ralph DeMarr, On partially ordering operator algebras, Canadian J. Math. 19 (1967), 636–643. MR 212579, DOI 10.4153/CJM-1967-057-6
- Ralph DeMarr, A generalization of the Perron-Frobenius theorem, Duke Math. J. 37 (1970), 113–120. MR 254592
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 255-260
- MSC: Primary 06A70
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313161-3
- MathSciNet review: 0313161