Geodesic
$*$-algebras of unbounded operators affiliated with a von Neumann algebra
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 183-197 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, the $*$-algebras of measurable operators, locally measurable operators, and $\tau$-measurable operators associated with von Neumann algebra $M$ are considered. Conditions under which some of these algebras coincide are given. 
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M. A. Muratov; V. I. Chilin. $*$-algebras of unbounded operators affiliated with a von Neumann algebra. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 183-197. http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a9/

[1] I. E. Segal, “A noncommutative extension of abstract integration”, Ann. Math., 57 (1953), 401–457 | DOI | MR | Zbl

[2] E. Nelson, “Notes on non-commutative integration”, J. Funct. Anal., 15 (1974), 103–116 | DOI | MR | Zbl

[3] F. J. Yeadon, “Non-commutative $L^P$-spaces”, Math. Proc. Camb. Phil. Soc., 77 (1975), 91–102 | DOI | MR | Zbl

[4] T. Fack, H. Kosaki, “Generalized $s$-numbers of $\tau$-mesaurable operators”, Pacific J. Math., 123 (1986), 269–300 | MR | Zbl

[5] P. G. Dixon, “Unbounded operator algebras”, Proc. London Math. Soc., 23 (1971), 53–59 | DOI | MR

[6] S. Sankaran, “The $*$-algebra of unbounded operators”, J. London Math. Soc., 34 (1959), 337–344 | DOI | MR | Zbl

[7] F. J. Yeadon, “Convergence of measurable operators”, Proc. Camb. Phil. Soc., 74 (1973), 257–268 | DOI | MR | Zbl

[8] B. S. Zakirov, V. I. Chilin, “Abstraktnaya kharakterizatsiya $EW^*$-algebr”, Funkts. anal. i ego prilozh., 25:1 (1991), 76–78 | MR | Zbl

[9] S. Stratila, L. Zsido, Lectures on von Neumann algebras, Abacus Press, 1979 | MR | Zbl

[10] M. Takesaki, Theory of operator algebras, I, Springer, New York, 1979 | MR

[11] K. Saito, “On the algebra of measurable operators for a general $AW^*$-algebra, II”, Tohoku. Math. J., 23 (1971), 525–534 | DOI | MR