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Fuglede-Putnam theorem for locally measurable operators


Authors: A. Ber, V. Chilin, F. Sukochev and D. Zanin
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
Published electronically: November 7, 2017
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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), suppl., 13-20. MR 3310055
  • [2] S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175-182. MR 0107826, https://doi.org/10.2307/2033572
  • [3] Jacques Dixmier, von Neumann algebras, with a preface by E. C. Lance, translated from the second French edition by F. Jellett, North-Holland Mathematical Library, vol. 27, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 641217
  • [4] Bent Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), 35-40. MR 0032944
  • [5] 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, https://doi.org/10.7900/jot.2015jan23.2065
  • [6] 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).
  • [7] Edward Nelson, Notes on non-commutative integration, J. Functional Analysis 15 (1974), 103-116. MR 0355628
  • [8] John von Neumann, Approximative properties of matrices of high finite order, Portugaliae Math. 3 (1942), 1-62. MR 0006137
  • [9] 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
  • [10] Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
  • [11] Shôichirô Sakai, $ C^*$-algebras and $ W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
  • [12] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401-457. MR 0054864, https://doi.org/10.2307/1969729
  • [13] Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
  • [14] F. J. Yeadon, Convergence of measurable operators, Proc. Cambridge Philos. Soc. 74 (1973), 257-268. MR 0326411
  • [15] 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, https://doi.org/10.1007/BF01090683

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Additional Information

A. Ber
Affiliation: Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tash- kent, 100174 Uzbekistan
Email: aber1960@mail.ru

V. Chilin
Affiliation: Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tash- kent, 100174 Uzbekistan
Email: chilin@ucd.uz

F. Sukochev
Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia
Email: f.sukochev@unsw.edu.au

D. Zanin
Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia
Email: d.zanin@unsw.edu.au

DOI: https://doi.org/10.1090/proc/13845
Keywords: Fuglede-Putnam theorem, von Neumann algebra, locally measurable operator.
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
Article copyright: © Copyright 2017 American Mathematical Society

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