# PROJECTIONS AND THE KADISON-SINGER PROBLEM

@article{Casazza2007PROJECTIONSAT, title={PROJECTIONS AND THE KADISON-SINGER PROBLEM}, author={Peter G. Casazza and Dan Edidin and Deepti Kalra and Vern I. Paulsen}, journal={Operators and Matrices}, year={2007}, pages={391-408} }

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.

## 34 Citations

### An introduction to the Kadison-Singer Problem and the Paving Conjecture

- Mathematics
- 2013

We give a gentle introduction to the famous Kadison-Singer problem, aimed at readers without much background in functional analysis or operator theory. We explain why this problem is equivalent to…

### Paving small matrices and the Kadison-Singer extension problem

- Mathematics
- 2010

We compute paving parameters for classes of small matrices and the matrices that yield them. The convergence to 1 or not of the sequence of these parameters is equivalent to the Kadison-Singer…

### 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…

### CONCRETE CONSTRUCTIONS OF NON-PAVABLE PROJECTIONS

- Mathematics
- 2009

It is known that the paving conjecture fails for 2-paving projections with constant diagonal 1/2. But the proofs of this fact are existence proofs. We will give concrete examples of these projections…

### The Kadison-Singer Problem

- Mathematics
- 2017

We give self-contained presentation of results related to the Kadison-Singer problem, which was recently solved by Marcus, Spielman, and Srivastava. This problem connects with unusually large number…

### 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…

### THE BOURGAIN-TZAFRIRI CONJECTURE AND CONCRETE CONSTRUCTIONS OF NON-PAVABLE PROJECTIONS

- Mathematics
- 2010

It is known that the Kadison-Singer Problem (KS) and the Paving Conjecture (PC) are equivalent to the Bourgain-Tzafriri Con- jecture (BT). Also, it is known that (PC) fails for 2-paving projections…

### Algorithmic constructions of unitary matrices and tight frames

- Computer Science
- 2011

A number of algorithms for constructing unitary matrices and tight frames with specialized properties, including the Kadison-Singer Problem and equiangular tight frames are given.

### PAVING AND THE KADISON-SINGER PROBLEM

- Mathematics

This is an introduction to problems surrounding the Paving Conjecture. 1. Paving Parameters and Notation Notation 1.1. Given an orthonormal basis {ei}i∈I for a Hilbert space H, for any A ⊂ I we…

### Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames

- Mathematics
- 2009

We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a Þxed orthonormal basis of a Hilbert…

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