Geodesic
Derivations with values in quasi-normed bimodules of locally measurable operators
Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 3-18.

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We prove that every derivation acting on a von Neumann algebra $\mathcal M$ with values in a quasi-normed bimodule of locally measurable operators affiliated with $\mathcal M$ is necessarily inner. 
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A. F. Ber; G. B. Levitina; V. I. Chilin. Derivations with values in quasi-normed bimodules of locally measurable operators. Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 3-18. http://geodesic.mathdoc.fr/item/MT_2014_17_1_a0/

[1] Bikchentaev A. M., “O minimalnosti topologii skhodimosti po mere na konechnykh algebrakh fon Neimana”, Matem. zametki, 75:3 (2004), 342–349 | DOI | MR | Zbl

[2] Muratov M. A., Chilin V. I., Algebry izmerimykh i lokalno izmerimykh operatorov, Tr. In-ta matematiki NAN Ukrainy, 69, Izd-vo In-ta matematiki NAN Ukrainy, Kiev, 2007

[3] Albeverio S., Ayupov Sh. A., Kudaybergenov K. K., “Derivations on the algebra of measurable operators affiliated with type I von Neumann algebras”, J. Funct. Anal., 256:9 (2009), 2917–2943 | DOI | MR | Zbl

[4] Ayupov Sh. A., Kudaybergenov K. K., “Derivations on algebras of measurable operators”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 13:2 (2010), 305–337 | DOI | MR | Zbl

[5] Ber A. F., Chilin V. I., Sukochev F. A., “Continuity of derivations of algebras of locally measurable operators”, Integral Equation Operator Theory, 75:4 (2013), 527–557 | DOI | MR | Zbl

[6] Ber A. F., Chilin V. I., Sukochev F. A., Innerness of Continuous Derivations on the Algebra of Locally Measurable Operators, 8 Apr 2013, arXiv: 1302.4883v2[math.OA] | MR

[7] Ber A. F., Sukochev F. A., “Commutator estimates in $W^*$-algebras”, J. Funct. Anal., 262:2 (2012), 537–568 | DOI | MR | Zbl

[8] Chilin V. I., Muratov M. A., “Comparison of topologies on $*$-algebras of locally measurable operators”, Positivity, 17:1 (2013), 111–132 | DOI | MR | Zbl

[9] Dodds P. G., Dodds T. K., de Pagter B., “Noncommutative Banach function spaces”, Math. Z., 201:4 (1989), 583–597 | DOI | MR | Zbl

[10] Kadison R. V., Ringrose J. R., Fundamentals of the Theory of Operator Algebras, v. II, Academic Press, Orlando, 1986 | MR | Zbl

[11] Kalton N. J., Peck N. T., Roberts J. W., An F-Space Sampler, London Math. Soc. Lecture Notes., 89, Cambridge Univ. Press, Cambridge, 1985 | DOI | MR

[12] Kalton N. J., Sukochev F. A., “Symmetric norms and spaces of operators”, J. Reine Angew. Math., 621 (2008), 81–121 | MR | Zbl

[13] Kaplansky I., “Any orthocomplemented complete modular lattice is a continuous geometry”, Ann. of Math., 61:2 (1955), 524–542 | DOI | MR

[14] Nelson E., “Notes on noncommutative integration”, J. Funct. Anal., 15 (1974), 103–116 | DOI | MR | Zbl

[15] Olesen D., “Derivations of $AW^*$-algebras are inner”, Pacific J. Math., 53:1 (1974), 555–561 | DOI | MR | Zbl

[16] Ringrose J. R., “Automatic continuity of derivations of operator algebras”, J. London Math. Soc., 5:2 (1972), 432–438 | DOI | MR | Zbl

[17] Rudin W., Functional Analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York–Dusseldorf–Johannesburg, 1973 | MR | Zbl

[18] Sakai S., $C^*$-Algebras and $W^*$-Algebras, Springer-Verlag, New York, 1971 | MR | Zbl

[19] Sankaran S., “The $^\ast$-algebra of unbounded operators”, J. London Math. Soc., 34 (1959), 337–344 | DOI | MR | Zbl

[20] Segal I. E., “A noncommutative extension of abstract integration”, Ann. of Math., 57:2 (1953), 401–457 | DOI | MR | Zbl

[21] Takesaki M., Theory of Operator Algebras, v. I, II, Springer-Verlag, New York–Heidelberg, 1979 | MR | Zbl

[22] Yeadon F. J., “Convergence of measurable operators”, Proc. Cambridge Philos. Soc., 74 (1973), 257–268 | DOI | MR | Zbl