Commutants of certain analytic operator algebras

Ji, Guoxing; Ohwada, Tomoyoshi; Saito, Kichi-Suke

doi:10.1090/S0002-9939-06-08326-2

Commutants of certain analytic operator algebras

Authors: Guoxing Ji, Tomoyoshi Ohwada and Kichi-Suke Saito
Journal: Proc. Amer. Math. Soc. 134 (2006), 2975-2982
MSC (2000): Primary 46L10, 46L55
DOI: https://doi.org/10.1090/S0002-9939-06-08326-2
Published electronically: May 4, 2006
MathSciNet review: 2231622
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that algebraic commutants of maximal subdiagonal algebras and of analytic operator algebras determined by flows in a $\sigma$ -finite von Neumann algebra are self-adjoint.

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Additional Information

Guoxing Ji
Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710062, People’s Republic of China
Email: gxji@snnu.edu.cn

Tomoyoshi Ohwada
Affiliation: Department of General Science, Tsuruoka National College of Technology, Tsuruoka, 997-8511, Japan
Email: ohwada@tsuruoka-nct.ac.jp

Kichi-Suke Saito
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
Email: saito@math.sc.niigata-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-06-08326-2
Keywords: Von Neumann algebra, subdiagonal algebra, analytic operator algebra, algebraic commutant
Received by editor(s): November 2, 2004
Received by editor(s) in revised form: April 29, 2005
Published electronically: May 4, 2006
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (No. 10571114) and the Excellent Young Teachers Program of MOE, P.R.C. The second author was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology. The third author was supported in part by a Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society