previous ::
next
The Calkin algebra has outer automorphisms
N. Christopher Phillips and Nik Weaver
Source: Duke Math. J. Volume 139, Number 1 (2007), 185-202.
Abstract
Assuming the continuum hypothesis, we show that the Calkin algebra has $2^{\aleph_1}$ outer automorphisms
Primary Subjects: 46L40
Secondary Subjects: 46L05, 03E50
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1184341242
Digital Object Identifier: doi:10.1215/S0012-7094-07-13915-2
Mathematical Reviews number (MathSciNet):
MR2322680
Zentralblatt MATH identifier:
05180738
References
C. A. Akemann and G. K. Pedersen, Central sequences and inner derivations of separable C*-algebras, Amer. J. Math. 101 (1979), 1047--1061.
Mathematical Reviews (MathSciNet):
MR0546302
Digital Object Identifier: doi:10.2307/2374125
W. Arveson, Notes on extensions of C*-algebras, Duke Math. J. 44 (1977), 329--355.
Mathematical Reviews (MathSciNet):
MR0438137
Digital Object Identifier: doi:10.1215/S0012-7094-77-04414-3
Project Euclid: euclid.dmj/1077312235
R. G. Bartle and L. M. Graves, Mappings between function spaces, Trans. Amer. Math. Soc. 72 (1952), 400--413.
Mathematical Reviews (MathSciNet):
MR0047910
Digital Object Identifier: doi:10.2307/1990709
L. G. Brown, R. G. Douglas, and P. A. Fillmore, ``Unitary equivalence modulo the compact operators and extensions of C*-algebras'' in Proceedings of a Conference on Operator Theory (Halifax, Nova Scotia, 1973), Lecture Notes in Math. 345, Springer, Berlin, 1973, 58--128.
Mathematical Reviews (MathSciNet):
MR0380478
—, Extensions of C*-algebras and $K$-homology, Ann. of Math. (2) 105 (1977), 265--324.
Mathematical Reviews (MathSciNet):
MR0458196
Digital Object Identifier: doi:10.2307/1970999
G. Elliott, personal communication, June 2006.
I. Farah, All automorphisms of the Calkin algebra are inner, preprint,\arxiv0705.3085v1[math.OA]
A. Ioana, J. Peterson, and S. Popa, Amalgamated free products of $w$-rigid factors and calculation of their symmetry groups, preprint,\arxivmath/0505589v5[math.OA]
G. Kuperberg, personal communication, June 1993.
V. Manuilov and K. Thomsen, $E$-theory is a special case of $KK$-theory, Proc. London Math. Soc. (3) 88 (2004), 455--478.
Mathematical Reviews (MathSciNet):
MR2032515
Digital Object Identifier: doi:10.1112/S0024611503014436
J. Mccarthy, personal communication, February 2006.
W. Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409--419.
Mathematical Reviews (MathSciNet):
MR0080902
Digital Object Identifier: doi:10.1215/S0012-7094-56-02337-7
Project Euclid: euclid.dmj/1077466953
S. Sakai, ``Pure states on C*-algebras'' in Advances in Quantum Dynamics (South Hadley, Mass., 2002), Contemp. Math. 335, Amer. Math. Soc., Providence, 2003, 247--251..
Mathematical Reviews (MathSciNet):
MR2029629
S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982.
Mathematical Reviews (MathSciNet):
MR0675955
S. Shelah and J. SteprāNs, PFA implies all automorphisms are trivial, Proc. Amer. Math. Soc. 104 (1988), 1220--1225.
Mathematical Reviews (MathSciNet):
MR0935111
Digital Object Identifier: doi:10.2307/2047617
ş. StrăTilă and L. Zsidó, Lectures on Von Neumann Algebras, rev. ed., Abacus, Tunbridge Wells, England, 1979.
Mathematical Reviews (MathSciNet):
MR0526399
B. VeličKović, OCA and automorphisms of $P(\omega)/\mathrmfin$, Topology Appl. 49 (1993), 1--13.
Mathematical Reviews (MathSciNet):
MR1202874
Digital Object Identifier: doi:10.1016/0166-8641(93)90127-Y
D. Voiculescu, A non-commutative Weyl --.von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97--113.
Mathematical Reviews (MathSciNet):
MR0415338
N. Weaver, Set theory and C*-algebras, Bull. Symbolic Logic 13 (2007), 1--20.
Mathematical Reviews (MathSciNet):
MR2300900
Digital Object Identifier: doi:10.2178/bsl/1174668215
Project Euclid: euclid.bsl/1174668215
previous ::
next
Duke Mathematical Journal