# 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}
}
• Published 2008
• Mathematics
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

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## References

SHOWING 1-10 OF 72 REFERENCES

### On a problem of Kadison and Singer.

• Mathematics
• 1991
In 1959, R. Kadison and I. Singer [10] raised the question whether every pure state (i.e. an extremal element in the space of states) on the C*-algebra D of the diagonal operators on (2 has a unique

### 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

• Mathematics
Abstract. We show that the Kadison-Singer problem is equivalent to the (strong) restricted invertibility conjecture of Bourgain-Tzafriri. We also show that these two problems are equivalent to two

### Frames and the Feichtinger conjecture

• Mathematics
• 2004
We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written

### John's decompositions: Selecting a large part

We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositionsid = ∑xj⊕xj, rather than on the coordinate one. The John's decomposition brings

### B(74) DOES NOT HAVE THE APPROXIMATION PROPERTY

• Mathematics
• 2006
In this paper we prove tha t B(74), the space of all bounded linear operators on a Hilbert space, does not have the approximation property (abbreviated throughout AP). The first example of a Banach

### Invertibility of ‘large’ submatrices with applications to the geometry of Banach spaces and harmonic analysis

• Mathematics
• 1987
AbstractThe main problem investigated in this paper is that of restricted invertibility of linear operators acting on finite dimensionallp-spaces. Our initial motivation to study such questions lies

### Stability theorems for Fourier frames and wavelet Riesz bases

In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type

### Matrix norm inequalities and the relative Dixmier property

• Mathematics
• 1988
AbstractIf x is a selfadjoint matrix with zero diagonal and non-negative entries, then there exists a decomposition of the identity into k diagonal orthogonal projections {pm} for which \parallel