Fuglede-Putnam theorem for locally measurable operators
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- by A. Ber, V. Chilin, F. Sukochev and D. Zanin PDF
- Proc. Amer. Math. Soc. 146 (2018), 1681-1692 Request permission
Abstract:
We extend the Fuglede-Putnam theorem from the algebra $B(H)$ of all bounded operators on the Hilbert space $H$ to the algebra of all locally measurable operators affiliated with a von Neumann algebra.References
- M. V. Ahramovich, V. I. Chilin, and M. A. Muratov, Fuglede-Putnam theorem in the algebra of locally measurable operators, Indian J. Math. 55 (2013), no. Fifth Dr. George Bachman Memorial Conference, suppl., 13–20. MR 3310055
- S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 107826, DOI 10.1090/S0002-9939-1959-0107826-9
- Jacques Dixmier, von Neumann algebras, North-Holland Mathematical Library, vol. 27, North-Holland Publishing Co., Amsterdam-New York, 1981. With a preface by E. C. Lance; Translated from the second French edition by F. Jellett. MR 641217
- Bent Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 35–40. MR 32944, DOI 10.1073/pnas.36.1.35
- Don Hadwin, Junhao Shen, Wenming Wu, and Wei Yuan, Relative commutant of an unbounded operator affiliated with a finite von Neumann algebra, J. Operator Theory 75 (2016), no. 1, 209–223. MR 3474104, DOI 10.7900/jot.2015jan23.2065
- M. A. Muratov and V.I. Chilin, Algebras of measurable and locally measurable operators, Proceedings of Institute of Mathematics of NAS of Ukraine, 2007, 69. (Russian).
- Edward Nelson, Notes on non-commutative integration, J. Functional Analysis 15 (1974), 103–116. MR 0355628, DOI 10.1016/0022-1236(74)90014-7
- John von Neumann, Approximative properties of matrices of high finite order, Portugal. Math. 3 (1942), 1–62. MR 6137
- C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag New York, Inc., New York, 1967. MR 0217618
- Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401–457. MR 54864, DOI 10.2307/1969729
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
- F. J. Yeadon, Convergence of measurable operators, Proc. Cambridge Philos. Soc. 74 (1973), 257–268. MR 326411, DOI 10.1017/s0305004100048052
- B. S. Zakirov and V. I. Chilin, Abstract characterization of $EW^\ast$-algebras, Funktsional. Anal. i Prilozhen. 25 (1991), no. 1, 76–78 (Russian); English transl., Funct. Anal. Appl. 25 (1991), no. 1, 63–64. MR 1113129, DOI 10.1007/BF01090683
Additional Information
- A. Ber
- Affiliation: Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tash- kent, 100174 Uzbekistan
- MR Author ID: 219337
- Email: aber1960@mail.ru
- V. Chilin
- Affiliation: Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tash- kent, 100174 Uzbekistan
- MR Author ID: 196460
- Email: chilin@ucd.uz
- F. Sukochev
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia
- MR Author ID: 229620
- Email: f.sukochev@unsw.edu.au
- D. Zanin
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia
- MR Author ID: 752894
- Email: d.zanin@unsw.edu.au
- Received by editor(s): January 5, 2017
- Received by editor(s) in revised form: June 7, 2017
- Published electronically: November 7, 2017
- Communicated by: Adrian Ioana
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1681-1692
- MSC (2010): Primary 46L60, 47C15, 47B15; Secondary 46L35, 46L89
- DOI: https://doi.org/10.1090/proc/13845
- MathSciNet review: 3754352