التفاصيل البيبلوغرافية
| العنوان: |
Continuous derivations on algebras of locally measurable operators are inner. |
| المؤلفون: |
Ber, A. F.1 ber@ucd.uz, Chilin, V. I.1, Sukochev, F. A.2 f.sukochev@unsw.edu.au |
| المصدر: |
Proceedings of the London Mathematical Society. Jul2014, Vol. 109 Issue 1, p65-89. 25p. |
| مصطلحات موضوعية: |
*ALGEBRA, *MATHEMATICAL proofs, *VON Neumann algebras, *TOPOLOGY, *BANACH algebras, *MATHEMATICAL models |
| مستخلص: |
We prove that every derivation acting on the $* $-algebra $LS({\mathscr {{M}}})$ of all locally measurable operators affiliated with a von Neumann algebra ${\mathscr {{M}}}$ is necessarily inner provided that it is continuous with respect to the local measure topology. In particular, every derivation on $LS({\mathscr {{M}}})$ is inner provided that ${\mathscr {{M}}}$ is a properly infinite von Neumann algebra. Furthermore, any derivation on an arbitrary von Neumann algebra ${\mathscr {{M}}}$ with values in a Banach ${\mathscr {{M}}}$-bimodule of locally measurable operators is inner. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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