Commutants of certain analytic operator algebras
HTML articles powered by AMS MathViewer
- by Guoxing Ji, Tomoyoshi Ohwada and Kichi-Suke Saito
- Proc. Amer. Math. Soc. 134 (2006), 2975-2982
- DOI: https://doi.org/10.1090/S0002-9939-06-08326-2
- Published electronically: May 4, 2006
- PDF | Request permission
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.References
- M. Anoussis, A. Katavolos, and M. Lambrou, On the reflexive algebra with two invariant subspaces, J. Operator Theory 30 (1993), no. 2, 267–299. MR 1305508
- William B. Arveson, Analyticity in operator algebras, Amer. J. Math. 89 (1967), 578–642. MR 223899, DOI 10.2307/2373237
- William B. Arveson, Operator algebras and measure preserving automorphisms, Acta Math. 118 (1967), 95–109. MR 210866, DOI 10.1007/BF02392478
- William Arveson, On groups of automorphisms of operator algebras, J. Functional Analysis 15 (1974), 217–243. MR 0348518, DOI 10.1016/0022-1236(74)90034-2
- Ruy Exel, Maximal subdiagonal algebras, Amer. J. Math. 110 (1988), no. 4, 775–782. MR 955297, DOI 10.2307/2374650
- Frank Gilfeather and David R. Larson, Nest-subalgebras of von Neumann algebras: commutants modulo compacts and distance estimates, J. Operator Theory 7 (1982), no. 2, 279–302. MR 658614
- U. Haagerup, Non-commutative integration theory, unpublished manuscript, 1980.
- Guoxing Ji, Relative lattices of certain analytic operator algebras, Houston J. Math. 28 (2002), no. 1, 183–191. MR 1876948
- Guo Xing Ji and Hong Ke Du, Subdiagonal algebras with a factorization property, Acta Math. Sinica (Chinese Ser.) 46 (2003), no. 5, 883–890 (Chinese, with English and Chinese summaries). MR 2025391
- Guoxing Ji, Tomoyoshi Ohwada, and Kichi-Suke Saito, Certain structure of subdiagonal algebras, J. Operator Theory 39 (1998), no. 2, 309–317. MR 1620570
- Guoxing Ji, Tomoyoshi Ohwada, and Kichi-Suke Saito, Triangular forms of subdiagonal algebras, Hokkaido Math. J. 27 (1998), no. 3, 545–552. MR 1662955, DOI 10.14492/hokmj/1351001461
- Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. II, Pure and Applied Mathematics, vol. 100, Academic Press, Inc., Orlando, FL, 1986. Advanced theory. MR 859186, DOI 10.1016/S0079-8169(08)60611-X
- Shinzô Kawamura and Jun Tomiyama, On subdiagonal algebras associated with flows in operator algebras, J. Math. Soc. Japan 29 (1977), no. 1, 73–90. MR 454650, DOI 10.2969/jmsj/02910073
- Richard I. Loebl and Paul S. Muhly, Analyticity and flows in von Neumann algebras, J. Functional Analysis 29 (1978), no. 2, 214–252. MR 504460, DOI 10.1016/0022-1236(78)90007-1
- A. N. Loginov and V. S. Šul′man, Hereditary and intermediate reflexivity of $W^*$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 6, 1260–1273, 1437 (Russian). MR 0405124
- Baruch Solel, Maximality of analytic operator algebras, Israel J. Math. 62 (1988), no. 1, 63–89. MR 947830, DOI 10.1007/BF02767354
- Quanhua Xu, On the maximality of subdiagonal algebras, J. Operator Theory 54 (2005), no. 1, 137–146. MR 2168864
Bibliographic 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
- 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
- © Copyright 2006 American Mathematical Society
- 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
- MathSciNet review: 2231622