Some new equivalences of Anderson’s paving conjectures

@inproceedings{Paulsen2007SomeNE,
  title={Some new equivalences of Anderson’s paving conjectures},
  author={Vern I. Paulsen and M. Raghupathi},
  year={2007}
}
Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operators are paveable, then every 0 diagonal operator is paveable. This result follows from a new paving condition for positive operators. In addition, we prove that if the upper triangular Toeplitz operators are paveable, then all Toeplitz operators… 
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References

SHOWING 1-10 OF 14 REFERENCES
The paving conjecture is equivalent to the paving conjecture for triangular matrices
We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.
Logmodularity and isometries of operator algebras
We generalize some facts about function algebras to operator algebras, using the noncommutative Shilov boundary or C*-envelope first considered by Arveson. In the first part we study and characterize
Interpolation problems in nest algebras
A Conjecture Concerning the Pure States of B(H) and a Related Theorem
The purpose of this note is twofold. First to present a conjecture concerning the form of the pure states on B(H) and second to prove a theorem related to this conjecture.
Extensions, restrictions, and representations of states on *-algebras
In the first three sections the question of when a pure state g on a C*-subalgebra B of a C*-algebra A has a unique state extension is studied. It is shown that an extension/is unique if and only if
Analytic functions and logmodular Banach algebras
The first part of this paper presents a generalization of a portion of the theory of analytic functions in the unit disc. The theory to be extended consists of some basic theorems related to the
A conjecture concerning pure states of B(H) and related theorems, in Proceedings, Vth International Conference Operator Algebras, Timisoara and Herculane
  • 1984
Extreme points in sets of linear maps on B(H)
  • J. Func. Anal
  • 1979
...
...