Abstract:
We prove that every derivation acting on a von Neumann algebra M with values in a quasi-normed bimodule of locally measurable operators affiliated with M is necessarily inner.
Citation:
A. F. Ber, G. B. Levitina, V. I. Chilin, “Derivations with values in quasi-normed bimodules of locally measurable operators”, Mat. Tr., 17:1 (2014), 3–18; Siberian Adv. Math., 25:3 (2015), 169–178
This publication is cited in the following 8 articles:
A. M. Bikchentaev, M. F. Darwish, M. A. Muratov, “Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II”, Ann. Funct. Anal., 15:3 (2024)
A. M. Bikchentaev, “The topologies of local convergence in measure on the algebras of measurable operators”, Siberian Math. J., 64:1 (2023), 13–21
A. Ber, J. Huang, G. Levitina, F. Sukochev, “Derivations with Values in the Ideal of $\tau $-Compact Operators Affiliated with a Semifinite von Neumann Algebra”, Commun. Math. Phys., 390:2 (2022), 577
A. M. Bikchentaev, “Renormalizations of measurable operator ideal spaces affiliated to semi-finite von Neumann algebra”, Ufa Math. J., 11:3 (2019), 3–10
A. M. Bikchentaev, “Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra”, Siberian Math. J., 59:2 (2018), 243–251
A. A. Alimov, V. I. Chilin, “Differentsirovaniya so znacheniyami v idealnykh $F$-prostranstvakh izmerimykh funktsii”, Vladikavk. matem. zhurn., 20:1 (2018), 21–29
A. F. Ber, V. I. Chilin, F. A. Sukochev, “Derivations on Banach $*$-ideals in von Neumann algebras”, Vladikavk. matem. zhurn., 20:2 (2018), 23–28
A. Ber, J. Huang, G. Levitina, F. Sukochev, “Derivations with values in ideals of semifinite von Neumann algebras”, J. Funct. Anal., 272:12 (2017), 4984–4997
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