Graphs and CCR algebras
I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.
math.OA↗
arXiv subjects
Ilijas Farah
Publications and source records attributed to Ilijas Farah.
The commutant of L(H) in its ultrapower may or may not be trivial
Kirchberg asked in 2004 whether the commutant of L(H)$ in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter.
math.OA↗
Orthonormal bases of Hilbert spaces
I prove that a Hilbert space has the property that each of its dense (not necessarily closed) subspaces contains an orthoormal basis if and only if it is separable.
math.LO↗
The relative commutant of separable C*-algebras of real rank zero
We answer a question of E. Kirchberg (personal communication): does the relative commutant of a separable C*-algebra in its ultrapower depend on the choice of the ultrafilter?
math.OA↗
Between Maharam's and von Neumann's problems
If I is a suitably definable sigma-ideal on the real line and the factor algebra of Borel sets modulo I is weakly distributive then the algebra carries a Maharam submeasure.
math.LO↗