A Note On The KadisonSinger Problem
Abstract
Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H > H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider C(\beta N) as a subalgebra of B(H). For each t in \beta N, let [\delta_t] be the set of the states of B(H) that extend the Dirac measure \delta_t. Our main result shows that, for each t in \beta N, this set either lies in a finite dimensional subspace of B(H)* or else it must contain a homeomorphic copy of \beta N.
 Publication:

arXiv eprints
 Pub Date:
 August 2007
 DOI:
 10.48550/arXiv.0708.2366
 arXiv:
 arXiv:0708.2366
 Bibcode:
 2007arXiv0708.2366A
 Keywords:

 Mathematics  Operator Algebras;
 46L30;
 46L05