# Fe b 20 06 THE KADISON-SINGER PROBLEM IN MATHEMATICS AND ENGINEERING : A DETAILED ACCOUNT

@inproceedings{Casazza2008FeB2, title={Fe b 20 06 THE KADISON-SINGER PROBLEM IN MATHEMATICS AND ENGINEERING : A DETAILED ACCOUNT}, author={Peter G. Casazza and Matthew C. Fickus and Janet C. Tremain and Eric S. Weber}, year={2008} }

We will show that the famous, intractible 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. This gives all these areas common ground on which to interact as well as explaining why each of these areas has volumes of literature on their respective problems without a satisfactory resolution. In each of these areas we will reduce the problem to the minimum which needs to be…

## 11 Citations

### Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem

- Mathematics
- 2013

We use the method of interlacing polynomials introduced in our previous article to prove two theorems known to imply a positive solution to the Kadison{Singer problem. The rst is Weaver’s conjecture…

### A decomposition theorem for frames and the Feichtinger Conjecture

- Mathematics
- 2007

In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C*-Algebras. We will show that every bounded Bessel…

### Is the Algorithmic Kadison-Singer Problem Hard?

- Computer Science, MathematicsArXiv
- 2022

A randomised algorithm with one-sided error for the KS 2 ( c ) problem that has running time O for the Kadison-Singer problem whose running time is quasi-polynomial in m in a certain regime, although having exponential dependency on d .

### Improved bounds in Weaver and Feichtinger conjectures

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

We sharpen the constant in the
{\mathrm{KS}_{2}}
Conjecture of Weaver [31] that was given by Marcus, Spielman and Srivastava [28] in their solution of the Kadison–Singer problem.
We then…

### Discrete Hilbert transforms on sparse sequences

- Mathematics
- 2009

Weighted discrete Hilbert transforms (an)n ↦ ∑n an vn/(z−γn) from ℓ2ν to a weighted L2‐space are studied, with Γ=(γn) a sequence of distinct points in the complex plane and v=(vn) a corresponding…

### THE KADISON-SINGER PROBLEM AND THE UNCERTAINTY PRINCIPLE

- Mathematics
- 2008

We compare and contrast the Kadison-Singer problem to the Uncertainty Principle via exponential frames. Our results suggest that the Kadison-Singer problem, if true, is in a sense a stronger version…

### A II1 Factor Approach to the Kadison–Singer Problem

- Materials ScienceCommunications in Mathematical Physics
- 2014

We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra ℓ∞N⊂B(ℓ2N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

### Optimal Arithmetic Structure in Exponential Riesz Sequences

- Materials ScienceJournal of Fourier Analysis and Applications
- 2020

We consider exponential systems EΛ=eiλtλ∈Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Kesten–McKay Law for Random Subensembles of Paley Equiangular Tight Frames

- MathematicsConstructive Approximation
- 2020

We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames.…

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### A decomposition theorem for frames and the Feichtinger Conjecture

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In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C*-Algebras. We will show that every bounded Bessel…

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