Property 𝐿 and asymptotic abelianness for von Neumann algebras of type 𝐼

Kawamura, Shinzō

doi:10.1090/S0002-9939-1982-0640232-X

Property $\textrm {L}$ and asymptotic abelianness for von Neumann algebras of type $\textrm {I}$
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Proc. Amer. Math. Soc. 84 (1982), 365-369 Request permission

Abstract:

We prove a correct assertion on Property L for von Neumann algebras of type I: a type I von Neumann algebra $M$ on a separable Hilbert space has Property L if and only if $M$ contains no minimal projection. Furthermore, a correct proof of an assertion on asymptotic abelianness for von Neumann algebras of type I is also given.

References

L. Pukánszky, Some examples of factors, Publ. Math. Debrecen 4 (1956), 135–156. MR 80894
Edward Sarian, Property $L$ and $W^{\ast }$-algebras of type $\textrm {I}$, Tohoku Math. J. (2) 31 (1979), no. 4, 491–494. MR 558679, DOI 10.2748/tmj/1178229732
Edward Sarian, Property $L$ and asymptotic abelianness for $W^{\ast }$-algebras, Proc. Amer. Math. Soc. 80 (1980), no. 1, 125–129. MR 574521, DOI 10.1090/S0002-9939-1980-0574521-2
Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728, DOI 10.1007/978-1-4612-6188-9
Jun Tomiyama, On the tensor products of von Neumann algebras, Pacific J. Math. 30 (1969), 263–270. MR 246141, DOI 10.2140/pjm.1969.30.263
Paul Willig, $B(H)$ is very noncommutative, Proc. Amer. Math. Soc. 24 (1970), 204–205. MR 248537, DOI 10.1090/S0002-9939-1970-0248537-3