m at h . FA ] 1 6 Ja n 20 07 PROJECTIONS AND THE KADISON - SINGER PROBLEM
نویسنده
چکیده
We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures.
منابع مشابه
The Other Kadison–singer Problem
Let H be `2 (over C) and let B(H) denote the C*-algebra of all bounded operators on H. Fix an orthonormal basis (en) for H. The atomic masa corresponding to this basis is `∞; equivalently, the algebra of all operators that are diagonalized by the basis (en). The projections in `∞ are exactly the projections onto subspaces spanned by a subset of {en}. That is, P(`∞) ∼= P(N) (here P(A) denotes th...
متن کاملThe Kadison-Singer problem in discrepancy theory
We give a combinatorial form of the Kadison-Singer problem, a famous problem in C*-algebra. This combinatorial problem, which has several minor variations, is a discrepancy question about vectors in C n. Some partial results can be easily deduced from known facts in discrepancy theory. In its original form, the so-called Kadison-Singer problem [8] asks whether every pure state on an atomic maxi...
متن کاملEquivalents of the Kadison-singer Problem
In a series of papers it was recently shown that the 1959 Kadison-Singer Problem in C∗-Algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and engineering. Because of the length and depth of these papers, it has been difficult for people in the various impacted areas to get an overview of how their problems relate to the ...
متن کاملThe Kadison-singer Problem and the Uncertainty Principle
We compare and contrast the Kadison-Singer problem to the Uncertainty Principle via exponential frames. Our results suggest that the KadisonSinger problem, if true, is in a sense a stronger version of the Uncertainty Principle. In 1959, Kadison and Singer answered in the negative [13] the well known question of unique pure state extensions: can a pure state on a C∗ subalgebra of B(H) be extende...
متن کاملKadison-Singer algebras: hyperfinite case.
A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...
متن کامل