Interpolation of Positive Operators
Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 43-58.

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We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces $L_1$, $L_\infty$ associated with weights and traces on von Neumann algebras.
Mots-clés : interpolation problem
Keywords: positive linear operators, ordered Banach spaces, Banach couple, von Neumann algebra.
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L. V. Veselova; F. A. Sukochev; O. E. Tikhonov. Interpolation of Positive Operators. Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 43-58. http://geodesic.mathdoc.fr/item/MZM_2007_81_1_a3/

[1] G. Ya. Lozanovskii, “Zamechanie ob odnoi interpolyatsionnoi teoreme Kalderona”, Funktsion. analiz i ego prilozh., 6:4 (1972), 89–90 | MR | Zbl

[2] B. Z. Vulikh, Vvedenie v teoriyu konusov v normirovannykh prostranstvakh, Kalininskii gos. un-t, Kalinin, 1977

[3] M. A. Krasnoselskii, E. A. Lifshits, A. V. Sobolev, Pozitivnye lineinye sistemy: metod polozhitelnykh operatorov, Nauka, M., 1985 | MR | Zbl

[4] L. Asimow, A. J. Ellis, Convexity Theory and its Applications in Functional Analysis, Academic Press, London, 1980 | MR | Zbl

[5] Y. A. Abramovich, C. D. Aliprantis, “Positive operators”, Handbook of the Geometry of Banach Spaces, Vol. I, eds. W. B. Johnson, J. Lindenstrauss, North-Holland, Amsterdam, 2001, 85–122 | MR | Zbl

[6] B. Z. Vulikh, Spetsialnye voprosy geometrii konusov v normirovannykh prostranstvakh, Kalininskii gos. un-t, Kalinin, 1978

[7] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR | Zbl

[8] A. V. Bukhvalov, V. B. Korotkov, A. G. Kusraev, S. S. Kutateladze, B. M. Makarov, Vektornye reshetki i integralnye operatory, Nauka. Sib. otd., Novosibirsk, 1992 | MR | Zbl

[9] N. Aronszajn, E. Gagliardo, “Interpolation spaces and interpolation methods”, Ann. Mat. Pura Appl. (4), 68 (1965), 51–117 | DOI | MR | Zbl

[10] Yu. A. Brudnyi, S. G. Krein, E. M. Semenov, “Interpolyatsiya lineinykh operatorov”, Itogi nauki i tekhn. Matem. analiz, 24, VINITI, M., 1986, 3–163 | MR | Zbl

[11] V. I. Ovchinnikov, “The method of orbits in interpolation theory”, Math. Rep., 1:2 (1984), 349–515, Harwood Academic Publishers | MR | Zbl

[12] M. Takesaki, Theory of Operator Algebras, I, Springer-Verlag, New York–Heidelberg, 1979 ; 2nd edition, Encyclopaedia of Math. Sci., 124, Springer-Verlag, Berlin, 2002 | MR | Zbl | MR | Zbl

[13] M. Takesaki, Theory of Operator Algebras, II, Encyclopaedia of Math. Sci., 125, Springer-Verlag, Berlin, 2003 | MR | Zbl

[14] N. V. Trunov, A. N. Sherstnev, “Vvedenie v teoriyu nekommutativnogo integrirovaniya”, Itogi nauki i tekhn. Sovr. probl. matematiki. Noveishie dostizheniya, 27, VINITI, M., 1985, 167–190 | MR | Zbl

[15] A. N. Sherstnev, “Ob odnom nekommutativnom analoge prostranstva $L_1$”, Matem. analiz, Izd-vo Kazanskogo un-ta, Kazan, 1978, 112–123 | MR | Zbl

[16] P. G. Dodds, T. K. Dodds, B. de Pagter, “Fully symmetric operator spaces”, Integral Equations Operator Theory, 15:6 (1992), 942–972 | DOI | MR | Zbl

[17] P. G. Dodds, T. K. Dodds, B. de Pagter, “Noncommutative Köthe duality”, Trans. Amer. Math. Soc., 339:2 (1993), 717–750 | DOI | MR | Zbl

[18] V. I. Ovchinnikov, “Simmetrichnye prostranstva izmerimykh operatorov”, Dokl. AN SSSR, 191:4 (1970), 769–771 | MR | Zbl

[19] V. I. Chilin, “Neravenstvo treugolnika v algebrakh lokalno izmerimykh operatorov”, Matem. analiz i algebra, Tr. TashGU, Tashkent, 1986, 77–81 | MR | Zbl

[20] C. A. Akemann, J. Anderson, G. K. Pedersen, “Triangle inequalities in operator algebras”, Linear and Multilinear Algebra, 11:2 (1982), 167–178 | DOI | MR | Zbl