×

Recent topics on \(C^*\)-algebras (consistency and independency) and Kadison-Singer problem. (English) Zbl 1199.46143

Dykema, Ken (ed.) et al., Von Neumann algebras in Sibiu. Proceedings of the conference, Sibiu, Romania, June 9–16, 2007. Bucharest: Theta (ISBN 978-973-87899-4-4). Theta Series in Advanced Mathematics 10, 103-109 (2008).
Summary: In [in: Advances in quantum dynamics. AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 16–20, 2002. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 335, 247–251 (2003; Zbl 1049.46046)], the author asked whether the Calkin algebra has an outer \(*\)-automorphism. Recently, N. C. Phillips and N. Weaver [Duke Math. J. 139, No. 1, 185–202 (2007; Zbl 1220.46040)] and I. Farah [All automorphisms on the Calkin algebra are inner, preprint, arXiv:0705.3085] have proved that the statement “the Calkin algebra has an outer \(*\)-automorphism” is independent of ZFC. First, we explain these matters briefly. Next, we discuss the outstanding problem of Kadison-Singer and show some new results on the problem.
For the entire collection see [Zbl 1162.46004].

MSC:

46L40 Automorphisms of selfadjoint operator algebras
46L05 General theory of \(C^*\)-algebras
03E35 Consistency and independence results
03E50 Continuum hypothesis and Martin’s axiom
PDFBibTeX XMLCite