Abstract
Given a von Neumann algebra M with a faithful normal semifinite trace τ, let L(M, τ) be the algebra of all τ-measurable operators affiliated with M. We prove that if A is a locally convex reflexive complete metrizable solid *-subalgebra in L(M, τ), that can be embedded into a locally bounded weak Fréchet M-bimodule, then any derivation on A is inner.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Z. Abdullaev, The Dual Space for Arens Algebra, Uzbek Math. J. 2, 3 (1997).
S. Albeverio, Sh. A. Ayupov, and K. K. Kudaybergenov, Non Commutative Arens Algebras and Their Derivations, J. Funct. Anal. 253(1), 287 (2007).
S. Albeverio, Sh. A. Ayupov, and K. K. Kudaybergenov, Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra, SFB 611, Universität Bonn, Preprint, No. 301 (2006); arxivmath.OA/070317lvl
S. Albeverio, Sh. A. Ayupov, and K. K. Kudaybergenov, Descriptions of Derivations on Measurable Operator Algebras of Type I, SFB 611, Universität Bonn, Preprint, No. 361 (2007); arXivmath.OA/0710.3344vl
Sh. A. Ayupov, Derivations in Measurable Operator Algebras, DAN RUz 3, 14 (2000).
Sh. A. Ayupov, Derivations on Unbounded Operators Algebras, Abstracts of the International Conference “Operators Algebras and Quantum Probability” (Tashkent, 2005), p. 38–42.
A. F. Ber, V. I. Chilin, and F. A. Sukochev, Non-trivial Derivation on Commutative Regular Algebras. Extracta Math. 21(2), 107 (2006).
H. G. Dales, Banach Algebras and Automatic Continuity (Clarendon Press, Oxford, 2000).
A. Inoue, On a Class of Unbounded Operators II, Pacific J. Math. 66, 411 (1976).
A. G. Kusraev, Automorphisms and Derivations on a Universally Complete Complex f-Algebra, Sib. Math. J. 47, 77 (2006).
I. Namioka, E. Asplund, A Geometric Proof of Ryll-Nardzewski Fixed Point Theorem, Bull. Am. Math. Soc. 67, 443 (1967).
E. Nelson, Notes on Non-commutative Integration, J. Funct. Anal. 15, 91 (1975).
S. Sakai, C*-algebras and W*-algebras (Springer-Verlag, 1971).
S. Sakai, Operator Algebras in Dynamical Systems (Cambridge University Press, 1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted by O.E. Tikhonov
Rights and permissions
About this article
Cite this article
Ayupov, S.A., Kudaybergenov, K.K. Innerness of derivations on subalgebras of measurable operators. Lobachevskii J Math 29, 60–67 (2008). https://doi.org/10.1134/S1995080208020030
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080208020030