Disjointness preserving and diffuse operators
Huijsmans, C. B. ; de Pagter, B.
Compositio Mathematica, Tome 80 (1991), p. 351-374 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1991-01-01
@article{CM_1991__79_3_351_0,
     author = {Huijsmans, C. B. and de Pagter, B.},
     title = {Disjointness preserving and diffuse operators},
     journal = {Compositio Mathematica},
     volume = {80},
     year = {1991},
     pages = {351-374},
     mrnumber = {1121143},
     zbl = {0757.47023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1991__79_3_351_0}
}

Huijsmans, C. B.; de Pagter, B. Disjointness preserving and diffuse operators. Compositio Mathematica, Tome 80 (1991) pp. 351-374. http://gdmltest.u-ga.fr/item/CM_1991__79_3_351_0/

[Ab] Y.A. Abramovich, Multiplicative representation of disjointness preserving operators, Indag. Math. 45 (1983), 265-279. | MR 718068 | Zbl 0527.47025

[AB] C D. Aliprantis, O. Burkinshaw, Positive Operators, Academic Press, Orlando (1985). | MR 809372 | Zbl 0608.47039

[A1] W. Arendt, Ueber das Spektrum regulärer Operatoren, thesis, Tübingen (1979).

[A2] W. Arendt, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), 193-215. | MR 690185 | Zbl 0488.47016

[AH] W. Arendt, D.R. Hart, The spectrum of quasi-invertible disjointness preserving operators, J. Funct. An. 68 (1986), 149-167. | MR 852658 | Zbl 0611.47030

[BR1] G.J.H.M. Buskes, Van Rooij A.C.M., Hahn-Banach for Riesz homomorphisms, Indag. Math. 51 (1989), 25-34. | MR 993676 | Zbl 0683.46007

[BR2] G.J.H.M. Buskes, A.C.M. Van Rooij, Small Riesz spaces, Math. Proc. Camb. Phil. Soc. 105 (1989), 523-536. | MR 985689 | Zbl 0683.46013

[G] H. Gordon, Decomposition of linear functionals in Riesz spaces, Duke Math. J. 27 (1960), 597-606. | MR 117525 | Zbl 0107.08604

[H1] D.R. Hart, Disjointness preserving operators, thesis, Pasadena (1983).

[H2] D.R. Hart, Some properties of disjointness preserving operators, Indag. Math. 47 (1985), 183-197. | MR 799079 | Zbl 0576.47021

[HP] C.B. Huijsmans, B. De Pagter, The inverse of an orthomorphism, preprint 8, Leiden (1988).

[HS] E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer, Berlin (1965). | MR 367121 | Zbl 0137.03202

[L] W.A.J. Luxemburg, University of Arkansas Lecture Notes 4, Fayetteville (1979). | MR 568706 | Zbl 0431.46003

[LS] W.A.J. Luxemburg, A.R. Schep, A Radon Nikodym type theorem for positive operators and a dual, Indag. Math. 40 (1978), 357-375. | MR 507829 | Zbl 0389.47018

[LZ] W.A.J. Luxemburg, A.C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam (1971). | MR 511676 | Zbl 0231.46014

[M] M. Meyer, Les homomorphismes d'espaces vectoriels réticulés complexes, C.R. Acad. Sc. Paris 292 (1981), 793-796. | MR 622421 | Zbl 0467.46007

[P1] B. De Pagter, Compact Riesz homomorphisms, preprint Leiden (1979).

[P2] B. De Pagter, A note on disjointness preserving operators, Proc. Amer. Math. Soc. 90 (1984), 543-549. | MR 733403 | Zbl 0541.47032

[PS] B De Pagter, A. R. Schep, Measures of non-compactness of operators on Banach lattices, J. Funct. Anal. 78 (1988), 31-55. | MR 937631 | Zbl 0651.47023

[PW] B. De Pagter, W. Wnuk, Some remarks on Banach lattices with non-atomic duals, Indag. Math., New Series 1 (1990), 391-395. | MR 1075887 | Zbl 0731.46008

[S1] A.R. Schep, Order continuous components of operators and measures, Indag. Math. 40 (1978), 110-117. | MR 477876 | Zbl 0374.47016

[S2] A.R. Schep, Positive diagonal and triangular operators, J. Operator Theory 3 (1980), 165-178. | MR 578937 | Zbl 0452.47040

[Sch] H.H. Schaefer, Banach Lattices and Positive Operators, Grundlehren 215, Springer, Berlin (1974). | MR 423039 | Zbl 0296.47023

[V1] J. Voigt, The projection onto the center of operators in a Banach lattice, Math. Z. 199 (1988), 115-117. | MR 954756 | Zbl 0631.47027

[V2] J. Voigt, A note on the projection onto the center of operators in a Banach lattice, preprint Oldenburg (1989). | MR 954756

[W1] L.W. Weis, Decompositions of positive operators, North-Holland Mathematical Studies 90, Functional Analysis: Surveys and recent results III, 95-115, Amsterdam (1984). | MR 761375 | Zbl 0549.47016

[W2] L.W. Weis, On the representation of order continuous operators by random measures, Trans. Amer. Math. Soc. 285 (1984), 535-563. | MR 752490 | Zbl 0599.47042

[Wi] A.W. Wickstead, Extremal structure of cones of operators, Quart. J. Math. Oxford 32 (1981), 239-253. | MR 615198 | Zbl 0431.47024

[Z] A.C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam (1983). | MR 704021 | Zbl 0519.46001