12 Citations
The Kadison–Singer and Paulsen Problems in Finite Frame Theory
- Mathematics
- 2013
We now know that some of the basic open problems in frame theory are equivalent to fundamental open problems in a dozen areas of research in both pure and applied mathematics, engineering, and…
Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem
- Mathematics
- 2016
It is known that the famous, intractable 1959 Kadison-Singer problem in C∗-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied…
Topological Dynamics and Algebra in the Spectrum of L infinity of a locally compact Group: With Application to Crossed Products
- Mathematics
- 2009
In this text, I will look at some new approaches that may shed some light on the Kadison Singer problem, mainly one instigated by Vern Paulsen using dynamical systems in the Stone-Cech…
The Feichtinger Conjecture for Exponentials
- Mathematics
- 2010
The Feichtinger conjecture for exponentials asserts that the following property holds for every fat Cantor subset B of the circle group: the set of restrictions to B of exponential functions can be…
Syndetic sets, paving and the Feichtinger conjecture
- Mathematics
- 2010
We prove that if a Bessel sequence in a Hilbert space that is indexed by a countably infinite group in an invariant manner can be partitioned into finitely many Riesz basic sequences, then each of…
TITLE : THE FEICHTINGER CONJECTURE FOR EXPONENTIALS
- Mathematics
- 2010
The Feichtinger conjecture for exponentials asserts that the following property holds for every fat Cantor subset B of the circle group: the set of restrictions to B of exponential functions can be…
Tutorial on Rational Rotation $C^*$--Algebras
- Mathematics
- 2021
The rotation algebra Aθ is the universal C ∗–algebra generated by unitary operators U, V satisfying the commutation relation UV = ωV U where ω = e. They are rational if θ = p/q with 1 ≤ p ≤ q − 1,…
D ec 2 01 0 TITLE : THE FEICHTINGER CONJECTURE FOR EXPONENTIALS
- Mathematics
- 2021
The Feichtinger conjecture for exponentials asserts that the following property holds for every fat Cantor subset B of the circle group: the set of restrictions to B of exponential functions can be…
Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems
- Mathematics
- 2012
In this article, using orbits of the dynamical system generated by the function F, operator representations of commutation relations XX* = F(X*X) and AB = BF(A) are studied and used to investigate…
Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras
- Mathematics
- 2014
We consider a family of associative algebras, defined as the quotient of a free algebra with the ideal generated by a set of multi-parameter deformed commutation relations between four generators…
References
SHOWING 1-10 OF 22 REFERENCES
Extensions, restrictions, and representations of states on *-algebras
- Mathematics
- 1979
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…
Ramsey Theoretic Consequences of Some New Results About Algebra in the Stone-Čech Compactification
- Mathematics
- 2005
Recently [4] we have obtained some new algebraic results about βN, the Stone-Cech compactification of the discrete set of positive integers and about βW , where W is the free semigroup over a…
The Stone-Cech Compactification
- Mathematics
- 1974
1. Development of the Stone-?ech Compactification.- Completely Regular Spaces.- ?X and the Extension of Mappings.- ?-Filters and ?-Ultrafilters.- ?X and Maximal Ideal Spaces.- Spaces of…
Some new equivalences of Anderson’s paving conjectures
- Mathematics
- 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.…
PROJECTIONS AND THE KADISON-SINGER PROBLEM
- Mathematics
- 2007
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…
Ultrafilters: Where topological dynamics = algebra = combinatorics
- Mathematics
- 1993
We survey some connections between topological dynamics, semigroups of ultrafilters, and combinatorics. As an application, we give a proof, based on ideas of Bergelson and Hindman, of the…
Topological dynamics
- Education, EconomicsScholarpedia
- 2008
This inspiring book becomes one that is very booming. After published, this book can steal the market and book lovers to always run out of this book. And now, we will not let you run out any more to…
A conjecture concerning pure states of B(H) and related theorems
- in: Proceedings, 5th International Conference Operator Algebras, Timisoara and Herculane, Romania, Pitman, New York/London
- 1984