von Neumann algebras which are second dual spaces

von Neumann algebras which are second dual spaces
HTML articles powered by AMS MathViewer

by Cho-Ho Chu

Proc. Amer. Math. Soc. 112 (1991), 999-1000

DOI: https://doi.org/10.1090/S0002-9939-1991-1068117-3

PDF | Request permission

A $\sigma$-finite von Neumann algebra is a second dual if and only if it is atomic.

References

Joel Anderson and John Bunce, A type $II_{\infty }$ factor representation of the Calkin algebra, Amer. J. Math. 99 (1977), no. 3, 515–521. MR 454668, DOI 10.2307/2373928
Cho-Ho Chu, A note on scattered $C^{\ast }$-algebras and the Radon-Nikodým property, J. London Math. Soc. (2) 24 (1981), no. 3, 533–536. MR 635884, DOI 10.1112/jlms/s2-24.3.533
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
A. Pełczyński, On Banach spaces containing $L_{1}(\mu )$, Studia Math. 30 (1968), 231–246. MR 232195, DOI 10.4064/sm-30-2-231-246
Haskell P. Rosenthal, On injective Banach spaces and the spaces $L^{\infty }(\mu )$ for finite measure $\mu$, Acta Math. 124 (1970), 205–248. MR 257721, DOI 10.1007/BF02394572
Shôichirô Sakai, On a problem of Calkin, Amer. J. Math. 88 (1966), 935–941. MR 208399, DOI 10.2307/2373089
A. I. Shtern, On the second conjugate of a von Neumann algebra, Funktsional. Anal. i Prilozhen. 16 (1982), no. 2, 90 (Russian). MR 659179
Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728