Positive maps on self-dual cones
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Abstract:
Different properties of maps on a self-dual cone which preserve the order and the orthogonal decomposition are studied: polar decomposition, link with the order isomorphisms, normality, extremality within the order preserving maps. A characterization of derivation preserving maps is given. The results generalize a previous approach by S. Yamamuro et al.References
- Huzihiro Araki, An application of Dye’s theorem on projection lattices to orthogonally decomposable isomorphisms, Pacific J. Math. 137 (1989), no. 1, 1–13. MR 983324
- Jean Béllissard, Bruno Iochum, and Ricardo Lima, Homogeneous and facially homogeneous self-dual cones, Linear Algebra Appl. 19 (1978), no. 1, 1–16. MR 573910, DOI 10.1016/0024-3795(78)90002-2
- Alain Connes, Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann, Ann. Inst. Fourier (Grenoble) 24 (1974), no. 4, x, 121–155 (1975) (French, with English summary). MR 377533
- Trien Bang Dang, Extremal maps of a Hilbert space equipped with a natural cone, Math. Z. 194 (1987), no. 1, 95–97. MR 871221, DOI 10.1007/BF01168008
- T. B. Dang and S. Yamamuro, On homomorphisms of an orthogonally decomposable Hilbert space, J. Funct. Anal. 68 (1986), no. 3, 366–373. MR 859140, DOI 10.1016/0022-1236(86)90103-5
- Richard V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math. (2) 56 (1952), 494–503. MR 51442, DOI 10.2307/1969657
- Fumio Hiai and Sadayuki Yamamuro, On homomorphisms of an orthogonally decomposable Hilbert space. III, J. Austral. Math. Soc. Ser. A 45 (1988), no. 3, 287–295. MR 957194
- Bruno Iochum, Cônes autopolaires et algèbres de Jordan, Lecture Notes in Mathematics, vol. 1049, Springer-Verlag, Berlin, 1984 (French). MR 764767, DOI 10.1007/BFb0071358
- Reiner Nagel and Heinrich Uhlig, An abstract Kato inequality for generators of positive operators semigroups on Banach lattices, J. Operator Theory 6 (1981), no. 1, 113–123. MR 637005
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
- Lothar M. Schmitt, A remark on Radon-Nikodým properties of ordered Hilbert spaces, Proc. Amer. Math. Soc. 105 (1989), no. 4, 938–940. MR 957266, DOI 10.1090/S0002-9939-1989-0957266-4
- Sadayuki Yamamuro, On orthogonally decomposable ordered Banach spaces, Bull. Austral. Math. Soc. 30 (1984), no. 3, 357–380. MR 766794, DOI 10.1017/S0004972700002082
- Sadayuki Yamamuro, Absolute values in orthogonally decomposable spaces, Bull. Austral. Math. Soc. 31 (1985), no. 2, 215–233. MR 788577, DOI 10.1017/S0004972700004706
- Sadayuki Yamamuro, Symmetry groups on ordered Banach spaces, Bull. Austral. Math. Soc. 33 (1986), no. 2, 177–187. MR 832519, DOI 10.1017/S000497270000304X —, On homomorphisms of an orthogonally decomposable Hilbert space. II, J. Austral. Math. Soc. 43 (1987).
- Fumio Hiai and Sadayuki Yamamuro, On homomorphisms of an orthogonally decomposable Hilbert space. III, J. Austral. Math. Soc. Ser. A 45 (1988), no. 3, 287–295. MR 957194
- S. Yamamuro, Sur les homomorphismes d’un espace de Hilbert orthogonalement décomposable. IV, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 5, 179–182 (French, with English summary). MR 903957 —, On homomorphisms of an orthogonally decomposable Hilbert space. V, Research reports, No. 39, Australian National University, 1986. —, Homomorphisms of an orthogonally decomposable Hilbert space, Research reports, No. 13, Australian National University, 1988.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 755-766
- MSC: Primary 46L70; Secondary 17C65, 46C99
- DOI: https://doi.org/10.1090/S0002-9939-1990-1017003-2
- MathSciNet review: 1017003