Derivations of $AW^{\ast }$-algebras
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- by James C. Deel PDF
- Proc. Amer. Math. Soc. 42 (1974), 85-95 Request permission
Abstract:
It is proved that every derivation on an $A{W^ \ast }$-algebra of type $\mathrm {II}_1$ with central trace is inner. The proof employs a result on the algebraic decomposition of such algebras which is of interest even in the ${W^ \ast }$ case.References
- S. K. Berberian, On the projection geometry of a finite $AW^*$-algebra, Trans. Amer. Math. Soc. 83 (1956), 493–509. MR 85482, DOI 10.1090/S0002-9947-1956-0085482-8
- J. Dixmier, Les anneaux d’opérateurs de classe finie, Ann. Sci. École Norm. Sup. (3) 66 (1949), 209–261 (French). MR 0032940, DOI 10.24033/asens.970
- J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151–182 (French). MR 48787
- Jacob Feldman, Embedding of $AW^*$ algebras, Duke Math. J. 23 (1956), 303–307. MR 78669
- Jacob Feldman, Nonseparability of certain finite factors, Proc. Amer. Math. Soc. 7 (1956), 23–26. MR 79742, DOI 10.1090/S0002-9939-1956-0079742-X
- James Glimm, A Stone-Weierstrass theorem for $C^{\ast }$-algebras, Ann. of Math. (2) 72 (1960), 216–244. MR 116210, DOI 10.2307/1970133
- Malcolm Goldman, Structure of $AW^*$-algebras. I, Duke Math. J. 23 (1956), 23–34. MR 73949
- Adrienne A. Hall, Derivations of certain $C^{\ast }$-algebras, J. London Math. Soc. (2) 5 (1972), 321–329. MR 374926, DOI 10.1112/jlms/s2-5.2.321
- Herbert Halpern, Embedding as a double commutator in a type I $AW^{\ast }$-algebra, Trans. Amer. Math. Soc. 148 (1970), 85–98. MR 256180, DOI 10.1090/S0002-9947-1970-0256180-X
- Irving Kaplansky, Algebras of type $\textrm {I}$, Ann. of Math. (2) 56 (1952), 460–472. MR 50182, DOI 10.2307/1969654
- Irving Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839–858. MR 58137, DOI 10.2307/2372552
- J. R. Ringrose, Automatic continuity of derivations of operator algebras, J. London Math. Soc. (2) 5 (1972), 432–438. MR 374927, DOI 10.1112/jlms/s2-5.3.432 S. Strǎtilǎ and L. Zsidó, An algebraic reduction theory for ${W^ \ast }$-algebras. I, J. Functional Analysis 11 (1972), 295-313. H. Takemoto and J. Tomiyama, On the reduction of finite von Neumann algebras (to appear).
- Masamichi Takesaki, On the cross-norm of the direct product of $C^{\ast }$-algebras, Tohoku Math. J. (2) 16 (1964), 111–122. MR 165384, DOI 10.2748/tmj/1178243737
- Masamichi Takesaki, The quotient algebra of a finite von Neumann algebra, Pacific J. Math. 36 (1971), 827–831. MR 281020, DOI 10.2140/pjm.1971.36.827
- Jørgen Vesterstrøm, Quotients of finite $W^{\ast }$-algebras, J. Functional Analysis 9 (1972), 322–335. MR 0296715, DOI 10.1016/0022-1236(72)90005-5
- Harold Widom, Embedding in algebras of type I, Duke Math. J. 23 (1956), 309–324. MR 78668
- Fred B. Wright, A reduction for algebras of finite type, Ann. of Math. (2) 60 (1954), 560—570. MR 65037, DOI 10.2307/1969851
- Ti Yen, Trace on finite $AW^*$-algebras, Duke Math. J. 22 (1955), 207–222. MR 69404
- Ti Yen, Quotient algebra of a finite $AW^*$-algebra, Pacific J. Math. 6 (1956), 389–395. MR 79735, DOI 10.2140/pjm.1956.6.389
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 85-95
- MSC: Primary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0343050-0
- MathSciNet review: 0343050